Wide field-of-view polarization switches and methods of fabricating liquid crystal optical elements with pretilt

ABSTRACT

A switchable optical assembly comprises a switchable waveplate configured to be electrically activated and deactivated to selectively alter the polarization state of light incident thereon. The switchable waveplate comprises first and second surfaces and a first liquid crystal layer disposed between the first and second surfaces. The first liquid crystal layer comprises a plurality of liquid crystal molecules that are rotated about respective axes parallel to a central axis, where the rotation varies with an azimuthal angle about the central axis. The switchable waveplate additionally comprises a plurality of electrodes to apply an electrical signal across said first liquid crystal layer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to U.S. ProvisionalPatent Application No. 62/685,858, filed Jun. 15, 2018, entitled “WIDEFIELD-OF-VIEW POLARIZATION SWITCHES AND METHODS OF FABRICATING LIQUIDCRYSTAL OPTICAL ELEMENTS WITH PRETITLT,” the content of which is herebyincorporated by reference herein in its entirety.

INCORPORATION BY REFERENCE

This application incorporates by reference the entirety of each of thefollowing patent applications: U.S. application Ser. No. 14/555,585filed on Nov. 27, 2014, published on Jul. 23, 2015 as U.S. PublicationNo. 2015/0205126; U.S. application Ser. No. 14/690,401 filed on Apr. 18,2015, published on Oct. 22, 2015 as U.S. Publication No. 2015/0302652;U.S. application Ser. No. 14/212,961 filed on Mar. 14, 2014, now U.S.Pat. No. 9,417,452 issued on Aug. 16, 2016; and U.S. application Ser.No. 14/331,218 filed on Jul. 14, 2014, published on Oct. 29, 2015 asU.S. Publication No. 2015/0309263; U.S. application Ser. No. 15/795,067filed on Oct. 26, 2017, published on May 24, 2018 as U.S. PublicationNo. 2018/0143470; U.S. application Ser. No. 15/815,449 filed on Nov. 16,2017, published on May 24, 2018 as U.S. Publication No. 2018/0143485;International Application No. PCT/US2018/057604 filed on Oct. 25, 2018,published on May 2, 2019 as International Publication No. WO2019/084334.

BACKGROUND Field

The present disclosure relates to display systems and, moreparticularly, to augmented and virtual reality display systems.

Description of the Related Art

Modern computing and display technologies have facilitated thedevelopment of systems for so called “virtual reality” or “augmentedreality” experiences, wherein digitally reproduced images or portionsthereof are presented to a user in a manner wherein they seem to be, ormay be perceived as, real. A virtual reality, or “VR”, scenariotypically involves presentation of digital or virtual image informationwithout transparency to other actual real-world visual input; anaugmented reality, or “AR”, scenario typically involves presentation ofdigital or virtual image information as an augmentation to visualizationof the actual world around the user. A mixed reality, or “MR”, scenariois a type of AR scenario and typically involves virtual objects that areintegrated into, and responsive to, the natural world. For example, inan MR scenario, AR image content may be blocked by or otherwise beperceived as interacting with objects in the real world.

Referring to FIG. 1, an augmented reality scene 10 is depicted wherein auser of an AR technology sees a real-world park-like setting 20featuring people, trees, buildings in the background, and a concreteplatform 30. In addition to these items, the user of the AR technologyalso perceives that he “sees” “virtual content” such as a robot statue40 standing upon the real-world platform 30, and a cartoon-like avatarcharacter 50 flying by which seems to be a personification of a bumblebee, even though these elements 40, 50 do not exist in the real world.Because the human visual perception system is complex, it is challengingto produce an AR technology that facilitates a comfortable,natural-feeling, rich presentation of virtual image elements amongstother virtual or real-world imagery elements.

Systems and methods disclosed herein address various challenges relatedto AR and VR technology.

SUMMARY

In one aspect, a switchable optical assembly comprises a switchablewaveplate configured to be electrically activated and deactivated toselectively alter the polarization state of light incident thereon. Theswitchable waveplate comprises first and second surfaces and a firstliquid crystal layer disposed between the first and second surfaces. Thefirst liquid crystal layer comprises a plurality of liquid crystalmolecules that are rotated about respective axes parallel to a centralaxis, where the rotation varies with an azimuthal angle about thecentral axis. The switchable waveplate additionally comprises aplurality of electrodes to apply an electrical signal across said firstliquid crystal layer.

In another aspect, a switchable optical assembly comprises a switchablewaveplate configured to be electrically activated and deactivated toselectively alter the polarization state of light incident thereon. Theswitchable waveplate comprises first and second surfaces and a liquidcrystal layer disposed between the first and second surfaces. The liquidcrystal layer comprises a plurality of liquid crystal molecules longerthan wide along respective longitudinal directions, where the liquidcrystal molecules are orientated such that the longitudinal directionsextend radially from an axis of the first and second surfaces and theliquid crystal layer in a plurality of radial directions from said axis.The switchable waveplate additionally comprises a plurality ofelectrodes to apply an electrical signal across said liquid crystallayer.

In another aspect, a method of fabricating an optical element comprisesproviding a substrate extending along a horizontal direction and havinga normal thereto directed in a vertical direction. The methodadditionally comprises providing a first vertical alignment layer andproviding a second horizontal alignment layer. The method furthercomprises providing a liquid crystal layer comprising liquid crystalmolecules with respect to the first vertical alignment layer and thesecond horizontal alignment layer such that the liquid crystal moleculesare oriented at an oblique angle with respect to the vertical andhorizontal directions. The first vertical alignment layer causes theliquid crystal molecules to be oriented more vertical than without thefirst vertical alignment layer and the second horizontal alignment layercauses the liquid crystal molecules to be more horizontal than withoutthe second horizontal alignment layer.

In another aspect, an optical element comprises a substrate extendingalong a horizontal direction and having a normal thereto directed in avertical direction. The optical element additionally comprises providinga first vertical alignment layer and providing a second horizontalalignment layer. The optical element further comprises a liquid crystallayer comprising liquid crystal molecules with respect to the firstvertical alignment layer and the second horizontal alignment layer suchthat the liquid crystal molecules are oriented at an oblique angle withrespect to the vertical and horizontal directions. The first verticalalignment layer causes the liquid crystal molecules to be oriented morevertical than without the first vertical alignment layer and the secondhorizontal alignment layer causes the liquid crystal molecules to bemore horizontal than without the second horizontal alignment layer.

For purposes of summarizing the invention and the advantages achievedover the prior art, certain objects and advantages are described herein.Of course, it is to be understood that not necessarily all such objectsor advantages need to be achieved in accordance with any particularembodiment. Thus, for example, those skilled in the art will recognizethat the invention may be embodied or carried out in a manner that canachieve or optimize one advantage or a group of advantages withoutnecessarily achieving other objects or advantages.

All of these embodiments are intended to be within the scope of theinvention herein disclosed. These and other embodiments will becomereadily apparent to those skilled in the art from the following detaileddescription having reference to the attached figures, the invention notbeing limited to any particular disclosed embodiment(s).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a user's view of augmented reality (AR) through an ARdevice.

FIG. 2 illustrates a conventional display system for simulatingthree-dimensional imagery for a user.

FIGS. 3A-3C illustrate relationships between radius of curvature andfocal radius.

FIG. 4A illustrates a representation of the accommodation-vergenceresponse of the human visual system.

FIG. 4B illustrates examples of different accommodative states andvergence states of a pair of eyes of the user.

FIG. 4C illustrates an example of a representation of a top-down view ofa user viewing content via a display system.

FIG. 4D illustrates another example of a representation of a top-downview of a user viewing content via a display system.

FIG. 5 illustrates aspects of an approach for simulatingthree-dimensional imagery by modifying wavefront divergence.

FIG. 6 illustrates an example of a waveguide stack for outputting imageinformation to a user.

FIG. 7 illustrates an example of exit beams outputted by a waveguide.

FIG. 8 illustrates an example of a stacked waveguide assembly in whicheach depth plane includes images formed using multiple differentcomponent colors.

FIG. 9A illustrates a cross-sectional side view of an example of a setof stacked waveguides that each includes an incoupling optical element.

FIG. 9B illustrates a perspective view of an example of the plurality ofstacked waveguides of FIG. 9A.

FIG. 9C illustrates a top-down plan view of an example of the pluralityof stacked waveguides of FIGS. 9A and 9B.

FIG. 9D illustrates an example of wearable display system.

FIG. 10 illustrates an example of a display system comprising a pair ofadaptive lens assemblies.

FIG. 11A illustrates an example of the display system of FIG. 10displaying virtual content to a user at a virtual depth plane.

FIG. 11B illustrates an example of the display system of FIG. 10providing a view of real world content to a user.

FIG. 12A illustrates an example of a waveplate lens assembly comprisingliquid crystals.

FIG. 12B illustrates an example of a switchable waveplate lenscomprising liquid crystals.

FIG. 13A illustrates a cross-sectional view of an example of aswitchable waveplate comprising a layer of twisted nematic liquidcrystals.

FIG. 13B illustrates an example of a switchable waveplate assemblycomprising the switchable waveplate of FIG. 13A interposed between apair of quarter waveplates in operation with the switchable waveplateactivated or deactivated.

FIG. 13C illustrates an example of the quarter waveplate comprising aplurality of layers of twisted nematic liquid crystal layers.

FIG. 13D illustrates an example of a switchable waveplate assemblycomprising the switchable waveplate of FIG. 13A interposed between apair of quarter waveplates integrated as a single stack using adhesivelayers.

FIG. 13E illustrates an example of a switchable waveplate assemblycomprising a layer of twisted nematic liquid crystals interposed betweena pair of quarter waveplates integrated as a single stack.

FIG. 13F illustrates an example of a switchable waveplate assemblycomprising a layer of twisted nematic liquid crystals interposed betweena pair of quarter waveplates of FIG. 13C integrated as a single stack.

FIG. 14A illustrates a perspective view of an example of one of a pairof transparent electrodes for switching a layer of liquid crystals.

FIG. 14B illustrates a perspective view of an example of the other of apair of transparent electrodes for switching a layer of liquid crystals.

FIG. 14C illustrates a perspective view of an example of a pair ofvertically separated transparent electrodes for switching a layer ofliquid crystals.

FIG. 15A illustrates a plan view of an example of a pair of horizontallyinterlaced transparent electrodes for switching a layer of liquidcrystals.

FIG. 15B illustrates a cross-sectional view of an example of aswitchable waveplate assembly including the pair of horizontallyinterlaced transparent electrodes of FIG. 15A.

FIG. 16A illustrates a plan view of an example of a waveplate lenscomprising liquid crystals.

FIG. 16B illustrates a plan view of an example of a waveplate lenscomprising liquid crystals.

FIG. 16C illustrates an example of a waveplate lens that providesdifferent optical power to diverge or converge light passingtherethrough depending on the polarization of light and the side onwhich the light is incident.

FIG. 16D illustrates an example of a waveplate lens that providesdifferent optical power to diverge or converge light passingtherethrough depending on the polarization of light and the side onwhich the light is incident.

FIG. 17A illustrates an example of an adaptive lens assembly comprisingwaveplate lenses and a switchable waveplate.

FIG. 17B illustrates an example of the adaptive lens assembly of FIG.17A in operation with the switchable waveplate activated.

FIG. 17C illustrates an example of the adaptive lens assembly of FIG.13A in operation with the switchable waveplate deactivated.

FIG. 18A illustrates an example of a display device comprising awaveguide between pair of adaptive lens assemblies each comprisingwaveplate lenses and a switchable waveplate, in operation with theswitchable waveplate activated.

FIG. 18B illustrates an example of the display device of FIG. 18A, inoperation with the switchable waveplate deactivated.

FIG. 19A illustrates a plan view of an example arrangement of liquidcrystal molecules closest to the substrate of a broadband waveplate lenscomprising liquid crystals.

FIG. 19B illustrates the broadband waveplate lens comprising liquidcrystals arranged as illustrated in FIG. 19A converging light having afirst circular polarization.

FIG. 19C illustrates the broadband waveplate lens comprising liquidcrystals arranged as illustrated in FIG. 19A diverging light having asecond circular polarization.

FIG. 20A illustrates a plan view of example arrangement of liquidcrystal molecules a broadband waveplate lens comprising a plurality oflayers of twisted nematic liquid crystals.

FIG. 20B illustrates a cross-sectional view of an example of a broadbandwaveplate lens comprising a plurality of layers of twisted nematicliquid crystals.

FIG. 21 illustrates a cross-sectional view of an example of a broadbandwaveplate lens comprising a layer of liquid crystals having increasingbirefringence with increasing wavelength.

FIG. 22A illustrates a cross-sectional view of an example of adeactivated switchable broadband waveplate lens diverging and flippingthe polarization of light having a first circular polarization.

FIG. 22B illustrates a cross-sectional view of an example of adeactivated switchable broadband waveplate lens converging and flippingthe polarization of light having a second circular polarization.

FIG. 22C illustrates a cross-sectional view of an example of anactivated switchable broadband waveplate lens passing circularlypolarized light without substantially converging or diverging whilepreserving the polarization thereof.

FIG. 23A illustrates an example of a broadband adaptive waveplate lensassembly comprising a pair of broadband switchable waveplate lenses, inoperation in which both switchable waveplate lenses are deactivated.

FIG. 23B illustrates the broadband adaptive waveplate lens assembly ofFIG. 23A, in operation with one of the switchable waveplate lensesactivated.

FIG. 23C illustrates the broadband adaptive waveplate lens assembly ofFIG. 23A, in operation with one of the switchable waveplate lensesactivated.

FIG. 23D illustrates an example of a broadband adaptive waveplate lensassembly comprising a pair of broadband switchable waveplate lenses, inoperation in which both switchable waveplate lenses are activated.

FIG. 24A illustrates an example of an integrated broadband adaptivewaveplate lens assembly comprising a switchable broadband waveplate lensinterposed between a pair of active broadband switchable waveplatelenses.

FIG. 24B illustrates the broadband adaptive waveplate lens assembly ofFIG. 24A in operation as combination of broadband half waveplate lenses.

FIG. 24C illustrates the broadband adaptive waveplate lens assembly ofFIG. 24B in operation with the switchable broadband waveplate activated.

FIG. 24D illustrates the broadband adaptive waveplate lens assembly ofFIG. 24B in operation with the switchable broadband waveplatedeactivated.

FIG. 25A illustrates simulated diffraction efficiency versus wavelengthwithin in the visible spectrum of the broadband adaptive waveplate lensassembly of FIG. 24A with the switchable broadband waveplate activated.

FIG. 25B illustrates simulated diffraction efficiency versus wavelengthwithin in the visible spectrum of the broadband adaptive waveplate lensassembly of FIG. 24A with the switchable broadband waveplatedeactivated.

FIG. 26A illustrates simulated actual versus target net optical power ofan example broadband adaptive waveplate lens assembly comprising threebroadband switchable waveplate lenses, using a single lens state andmultiple lens states for a blue wavelength.

FIG. 26B illustrates simulated actual versus target net optical power ofan example broadband adaptive waveplate lens assembly comprising threebroadband switchable waveplate lenses, using a single lens state andmultiple lens states for a green wavelength.

FIG. 26C illustrates simulated actual versus target net optical power ofan example broadband adaptive waveplate lens assembly comprising threebroadband switchable waveplate lenses, using a single lens state andmultiple lens states for a red wavelength.

FIG. 27A-27C illustrate an example fabrication method of a broadbandwaveplate or a broadband waveplate lens.

FIG. 28 illustrate an example method of configuring an alignment layerfor aligning liquid crystal molecules in broadband waveplates orbroadband waveplate lenses using a two-beam exposure.

FIGS. 29A-29B illustrate an example method of configuring an alignmentlayer for aligning liquid crystal molecules in broadband waveplates orbroadband waveplate lenses using a master lens.

FIGS. 30A-30B illustrate an example method of configuring a nanoimprintalignment layer for aligning liquid crystal molecules in broadbandwaveplates or broadband waveplate lenses using a master lens andone-beam exposure.

FIG. 30C illustrates an example nanoimprint alignment layer for aligningliquid crystal molecules of a broadband waveplate lens using the examplemethod of FIGS. 30A-30B.

FIGS. 31A-31C illustrate an example method of fabricating a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals using a gap fill process.

FIGS. 32A-32E illustrate an example method of fabricating a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals using a layer transferprocess.

FIG. 33 illustrates an example of a switchable broadband waveplatecomprising liquid crystals or a switchable broadband waveplate lenscomprising liquid crystals formed on a portion of a substrate.

FIG. 34 illustrates an example method of forming a switchable broadbandwaveplate comprising liquid crystals or a switchable broadband waveplatelens comprising liquid crystals on a portion of a substrate by selectivecoating.

FIGS. 35A-35C illustrate an example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate byblanket coating a layer of liquid crystals and subtractively removing.

FIG. 36A-36C illustrate an example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate byusing selective optical patterning of an alignment layer.

FIG. 37A-37B illustrate an example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate byusing selective nanoimprinting an alignment layer.

FIG. 38 illustrates an example of an adaptive lens assembly comprisingwaveplate lenses and a switchable waveplate receiving light from a widefield-of-view. Light from objects on the periphery of the field-of-vieware incident on the switchable waveplate at an angle, which decreasesthe efficiency at which the polarization is rotated. This adaptive lensproduces ghost images at the wrong depth plane when such an element isused as a variable focus element for an augmented reality device.

FIG. 39 is a plot that illustrates the efficiency at which theswitchable waveplate rotates polarization at different angles of lightincident thereon. The bright portions (e.g., at the periphery) indicatereduced efficiency.

FIG. 40 illustrates yet another example design for a switchablewaveplate configured to increase the efficiency of polarization rotationfor light from objects on the periphery of the field-of-view. Theswitchable waveplate includes a liquid crystal layer comprisingmolecules that are rotated about axes parallel to a central axis throughthe switchable waveplate. The amount of rotation and thus theorientation of the molecules varies with azimuthal angle about thecentral axis such that the elongated molecules generally form concentricrings about the central axis. The longitudinal direction 4332 ofmolecules may be arranged along at least 3, 4, 5, 6, 8, 9, 10, 12, 14,20, 40 or more (or any range between any of these values) concentricring shaped paths. This configuration increases the uniformity inefficiency of polarization rotation of the switchable waveplate even forhighly off-axis field-of-view angles.

FIG. 41 illustrates still another example design for a switchablewaveplate configured to increase the efficiency of polarization rotationfor light from objects on the periphery of the field-of-view. Theswitchable waveplate includes a liquid crystal layer comprisingmolecules longer than wide along a longitudinal direction thereof. Themolecules are orientated such that the longitudinal direction extendsradially from a central axis through the switchable waveplate for aplurality of radial directions from the central axis. This configurationalso increases the uniformity in efficiency of polarization rotation ofthe switchable waveplate even for highly off-axis field-of-view angles.

FIGS. 42A and 42B illustrate an example of the switchable waveplatecomprising a plurality of layers of twisted liquid crystal layers, withthe wide field-of-view structures similar to either FIG. 40 or FIG. 41,to provide broadband operation over wavelengths similar to FIG. 20B

FIGS. 43A-43D illustrate a method of aligning LC molecules using firstand alignment layers having different orientations comprising forexample vertical and horizontal alignment layers. In this example, thehorizontal alignment layer comprises patterned nano structures.

Throughout the drawings, reference numbers may be re-used to indicatecorrespondence between referenced elements. The drawings are provided toillustrate example embodiments described herein and are not intended tolimit the scope of the disclosure.

DETAILED DESCRIPTION

AR systems may display virtual content to a user, or viewer, while stillallowing the user to see the world around them. Preferably, this contentis displayed on a head-mounted display, e.g., as part of eyewear, thatprojects image information to the user's eyes. In addition, the displaymay also transmit light from the surrounding environment to the user'seyes, to allow a view of that surrounding environment. As used herein,it will be appreciated that a “head-mounted” or “head mountable” displayis a display that may be mounted on the head of a viewer or user.

In some AR systems, a plurality of waveguides may be configured to formvirtual images at a plurality of virtual depth planes (also referred tosimply a “depth planes” herein). Different waveguides of the pluralityof waveguides may have different optical powers and may be formed atdifferent distances from the user's eye. The display systems may alsoinclude a plurality lenses that provide or additionally provide opticalpowers. The optical powers of the waveguides and/or the lenses mayprovide images at different virtual depth planes. Undesirably, each ofthe waveguides and lenses may increase the overall thickness, weight andcost of the display.

Advantageously, in various embodiments described herein, an adaptivelens assembly may be utilized to provide variable optical power to,e.g., modify the wavefront divergence of light propagating through thelens assembly to provide virtual depth planes at different perceiveddistances from a user. The adaptive lens assembly may include a pair ofwaveplate lenses having a switchable waveplate disposed between them.Each of the first and second waveplate lenses may be configured to altera polarization state of the light passing therethrough, and theswitchable waveplate may be switchable between a plurality of states,e.g., a first state that allows light to pass without changing apolarization of the light and a second state that alters thepolarization of the light (e.g., by changing the handedness of thepolarization). In some embodiments, one or both of the waveplate lensesmay be switchable between these first and second states and theintervening switchable waveplate noted above may be omitted.

It will be appreciated that the adaptive lens assembly may comprise astack of a plurality of waveplate lenses and a plurality of switchablewaveplates. For example, the adaptive lens assembly may comprisemultiple subassemblies comprising a pair of waveplate lenses with anintervening switchable waveplate. In some embodiments, the adaptive lensassembly may include alternating waveplate lenses and switchablewaveplates. Advantageously, such alternating arrangement allows areduction in thickness and weight by having neighboring switchablewaveplates share a common waveplate lens. In some embodiments, byswitching the states of the various combinations of the switchableplates in the stack, more than two discrete levels of optical power maybe provided.

In some embodiments, the adaptive lens assembly forms a display devicewith a waveguide assembly to form images at different virtual depthplanes. In various embodiments, the display device comprises a pair ofadaptive lens assemblies interposed by a waveguide assembly. Thewaveguide assembly includes a waveguide configured to propagate light(e.g., visible light) therein (e.g., via total internal reflection) andto outcouple the light. For example, the light may be outcoupled alongan optical axis direction normal to a major surface of the waveguide.One of the pair of adaptive lens assemblies may be formed on a firstside of the waveguide assembly and may be configured to provide variableoptical power to modify the wavefront of light passing through theadaptive lens assembly to form images at each of a plurality of virtualdepth planes. For example, the adaptive lens assemblies may converge ordiverge outcoupled light received from the waveguide assembly. Tocompensate for modifications of real world views due to the convergenceor divergence of ambient light propagating through the adaptive lensassembly and/or the waveguide assembly, the other of the pair ofadaptive lens assemblies is additionally provided on a second side ofthe waveguide assembly opposite the first side. When the switchablewaveplates of each adaptive lens assembly assume a corresponding state,the adaptive lens assemblies may have optical powers with oppositesigns, such that the other of the adaptive lens assemblies correct fordistortions caused by the adaptive lens assembly on the first side ofthe waveguide assembly.

Advantageously, relative to a continuously variable adaptive lens havingcontinuously variable optical elements, utilizing a switchable waveplatethat is switchable between two states simplifies the driving of theadaptive lens assembly and reduces the computational power needed todetermine how to appropriately activate the adaptive lens assembly for adesired optical power. In addition, by allowing the adaptive lensassembly to modify the wavefront divergence of light outputted by awaveguide, the number waveguides needed to provide a plurality of depthplanes is reduced relative to an arrangement in which each waveguideprovides a particular amount of wavefront divergence.

Reference will now be made to the drawings, in which like referencenumerals refer to like parts throughout. Unless indicated otherwise, thedrawings are schematic not necessarily drawn to scale.

Example Display Systems

FIG. 2 illustrates a conventional display system for simulatingthree-dimensional imagery for a user. It will be appreciated that auser's eyes are spaced apart and that, when looking at a real object inspace, each eye will have a slightly different view of the object andmay form an image of the object at different locations on the retina ofeach eye. This may be referred to as binocular disparity and may beutilized by the human visual system to provide a perception of depth.Conventional display systems simulate binocular disparity by presentingtwo distinct images 190, 200 with slightly different views of the samevirtual object—one for each eye 210, 220—corresponding to the views ofthe virtual object that would be seen by each eye were the virtualobject a real object at a desired depth. These images provide binocularcues that the user's visual system may interpret to derive a perceptionof depth.

With continued reference to FIG. 2, the images 190, 200 are spaced fromthe eyes 210, 220 by a distance 230 on a z-axis. The z-axis is parallelto the optical axis of the viewer with their eyes fixated on an objectat optical infinity directly ahead of the viewer. The images 190, 200are flat and at a fixed distance from the eyes 210, 220. Based on theslightly different views of a virtual object in the images presented tothe eyes 210, 220, respectively, the eyes may naturally rotate such thatan image of the object falls on corresponding points on the retinas ofeach of the eyes, to maintain single binocular vision. This rotation maycause the lines of sight of each of the eyes 210, 220 to converge onto apoint in space at which the virtual object is perceived to be present.As a result, providing three-dimensional imagery conventionally involvesproviding binocular cues that may manipulate the vergence of the user'seyes 210, 220, and that the human visual system interprets to provide aperception of depth.

Generating a realistic and comfortable perception of depth ischallenging, however. It will be appreciated that light from objects atdifferent distances from the eyes have wavefronts with different amountsof divergence. FIGS. 3A-3C illustrate relationships between distance andthe divergence of light rays. The distance between the object and theeye 210 is represented by, in order of decreasing distance, R1, R2, andR3. As shown in FIGS. 3A-3C, the light rays become more divergent asdistance to the object decreases. Conversely, as distance increases, thelight rays become more collimated. Stated another way, it may be saidthat the light field produced by a point (the object or a part of theobject) has a spherical wavefront curvature, which is a function of howfar away the point is from the eye of the user. The curvature increaseswith decreasing distance between the object and the eye 210. While onlya single eye 210 is illustrated for clarity of illustration in FIGS.3A-3C and other figures herein, the discussions regarding eye 210 may beapplied to both eyes 210 and 220 of a viewer.

With continued reference to FIGS. 3A-3C, light from an object that theviewer's eyes are fixated on may have different degrees of wavefrontdivergence. Due to the different amounts of wavefront divergence, thelight may be focused differently by the lens of the eye, which in turnmay require the lens to assume different shapes to form a focused imageon the retina of the eye. Where a focused image is not formed on theretina, the resulting retinal blur acts as a cue to accommodation thatcauses a change in the shape of the lens of the eye until a focusedimage is formed on the retina. For example, the cue to accommodation maytrigger the ciliary muscles surrounding the lens of the eye to relax orcontract, thereby modulating the force applied to the suspensoryligaments holding the lens, thus causing the shape of the lens of theeye to change until retinal blur of an object of fixation is eliminatedor minimized, thereby forming a focused image of the object of fixationon the retina (e.g., fovea) of the eye. The process by which the lens ofthe eye changes shape may be referred to as accommodation, and the shapeof the lens of the eye required to form a focused image of the object offixation on the retina (e.g., fovea) of the eye may be referred to as anaccommodative state.

With reference now to FIG. 4A, a representation of theaccommodation-vergence response of the human visual system isillustrated. The movement of the eyes to fixate on an object causes theeyes to receive light from the object, with the light forming an imageon each of the retinas of the eyes. The presence of retinal blur in theimage formed on the retina may provide a cue to accommodation, and therelative locations of the image on the retinas may provide a cue tovergence. The cue to accommodation causes accommodation to occur,resulting in the lenses of the eyes each assuming a particularaccommodative state that forms a focused image of the object on theretina (e.g., fovea) of the eye. On the other hand, the cue to vergencecauses vergence movements (rotation of the eyes) to occur such that theimages formed on each retina of each eye are at corresponding retinalpoints that maintain single binocular vision. In these positions, theeyes may be said to have assumed a particular vergence state. Withcontinued reference to FIG. 4A, accommodation may be understood to bethe process by which the eye achieves a particular accommodative state,and vergence may be understood to be the process by which the eyeachieves a particular vergence state. As indicated in FIG. 4A, theaccommodative and vergence states of the eyes may change if the userfixates on another object. For example, the accommodated state maychange if the user fixates on a new object at a different depth on thez-axis.

Without being limited by theory, it is believed that viewers of anobject may perceive the object as being “three-dimensional” due to acombination of vergence and accommodation. As noted above, vergencemovements (e.g., rotation of the eyes so that the pupils move toward oraway from each other to converge the lines of sight of the eyes tofixate upon an object) of the two eyes relative to each other areclosely associated with accommodation of the lenses of the eyes. Undernormal conditions, changing the shapes of the lenses of the eyes tochange focus from one object to another object at a different distancewill automatically cause a matching change in vergence to the samedistance, under a relationship known as the “accommodation-vergencereflex.” Likewise, a change in vergence will trigger a matching changein lens shape under normal conditions.

With reference now to FIG. 4B, examples of different accommodative andvergence states of the eyes are illustrated. The pair of eyes 222 a isfixated on an object at optical infinity, while the pair eyes 222 b arefixated on an object 221 at less than optical infinity. Notably, thevergence states of each pair of eyes is different, with the pair of eyes222 a directed straight ahead, while the pair of eyes 222 converge onthe object 221. The accommodative states of the eyes forming each pairof eyes 222 a and 222 b are also different, as represented by thedifferent shapes of the lenses 210 a, 220 a.

Undesirably, many users of conventional “3-D” display systems find suchconventional systems to be uncomfortable or may not perceive a sense ofdepth at all due to a mismatch between accommodative and vergence statesin these displays. As noted above, many stereoscopic or “3-D” displaysystems display a scene by providing slightly different images to eacheye. Such systems are uncomfortable for many viewers, since they, amongother things, simply provide different presentations of a scene andcause changes in the vergence states of the eyes, but without acorresponding change in the accommodative states of those eyes. Rather,the images are shown by a display at a fixed distance from the eyes,such that the eyes view all the image information at a singleaccommodative state. Such an arrangement works against the“accommodation-vergence reflex” by causing changes in the vergence statewithout a matching change in the accommodative state. This mismatch isbelieved to cause viewer discomfort. Display systems that provide abetter match between accommodation and vergence may form more realisticand comfortable simulations of three-dimensional imagery.

Without being limited by theory, it is believed that the human eyetypically may interpret a finite number of depth planes to provide depthperception. Consequently, a highly believable simulation of perceiveddepth may be achieved by providing, to the eye, different presentationsof an image corresponding to each of these limited numbers of depthplanes. In some embodiments, the different presentations may provideboth cues to vergence and matching cues to accommodation, therebyproviding physiologically correct accommodation-vergence matching.

With continued reference to FIG. 4B, two depth planes 240, correspondingto different distances in space from the eyes 210, 220, are illustrated.For a given depth plane 240, vergence cues may be provided by thedisplaying of images of appropriately different perspectives for eacheye 210, 220. In addition, for a given depth plane 240, light formingthe images provided to each eye 210, 220 may have a wavefront divergencecorresponding to a light field produced by a point at the distance ofthat depth plane 240.

In the illustrated embodiment, the distance, along the z-axis, of thedepth plane 240 containing the point 221 is 1 m. As used herein,distances or depths along the z-axis may be measured with a zero-pointlocated at the exit pupils of the user's eyes. Thus, a depth plane 240located at a depth of 1 m corresponds to a distance of 1 m away from theexit pupils of the user's eyes, on the optical axis of those eyes withthe eyes directed towards optical infinity. As an approximation, thedepth or distance along the z-axis may be measured from the display infront of the user's eyes (e.g., from the surface of a waveguide), plus avalue for the distance between the device and the exit pupils of theuser's eyes. That value may be called the eye relief and corresponds tothe distance between the exit pupil of the user's eye and the displayworn by the user in front of the eye. In practice, the value for the eyerelief may be a normalized value used generally for all viewers. Forexample, the eye relief may be assumed to be 20 mm and a depth planethat is at a depth of 1 m may be at a distance of 980 mm in front of thedisplay.

With reference now to FIGS. 4C and 4D, examples of matchedaccommodation-vergence distances and mismatched accommodation-vergencedistances are illustrated, respectively. As illustrated in FIG. 4C, thedisplay system may provide images of a virtual object to each eye 210,220. The images may cause the eyes 210, 220 to assume a vergence statein which the eyes converge on a point 15 on a depth plane 240. Inaddition, the images may be formed by a light having a wavefrontcurvature corresponding to real objects at that depth plane 240. As aresult, the eyes 210, 220 assume an accommodative state in which theimages are in focus on the retinas of those eyes. Thus, the user mayperceive the virtual object as being at the point 15 on the depth plane240.

It will be appreciated that each of the accommodative and vergencestates of the eyes 210, 220 are associated with a particular distance onthe z-axis. For example, an object at a particular distance from theeyes 210, 220 causes those eyes to assume particular accommodativestates based upon the distances of the object. The distance associatedwith a particular accommodative state may be referred to as theaccommodation distance, A_(d). Similarly, there are particular vergencedistances, V_(d), associated with the eyes in particular vergencestates, or positions relative to one another. Where the accommodationdistance and the vergence distance match, the relationship betweenaccommodation and vergence may be said to be physiologically correct.This is considered to be the most comfortable scenario for a viewer.

In stereoscopic displays, however, the accommodation distance and thevergence distance may not always match. For example, as illustrated inFIG. 4D, images displayed to the eyes 210, 220 may be displayed withwavefront divergence corresponding to depth plane 240, and the eyes 210,220 may assume a particular accommodative state in which the points 15a, 15 b on that depth plane are in focus. However, the images displayedto the eyes 210, 220 may provide cues for vergence that cause the eyes210, 220 to converge on a point 15 that is not located on the depthplane 240. As a result, the accommodation distance corresponds to thedistance from the exit pupils of the eyes 210, 220 to the depth plane240, while the vergence distance corresponds to the larger distance fromthe exit pupils of the eyes 210, 220 to the point 15, in someembodiments. The accommodation distance is different from the vergencedistance. Consequently, there is an accommodation-vergence mismatch.Such a mismatch is considered undesirable and may cause discomfort inthe user. It will be appreciated that the mismatch corresponds todistance (e.g., V_(d)−A_(d)) and may be characterized using diopters.

In some embodiments, it will be appreciated that a reference point otherthan exit pupils of the eyes 210, 220 may be utilized for determiningdistance for determining accommodation-vergence mismatch, so long as thesame reference point is utilized for the accommodation distance and thevergence distance. For example, the distances could be measured from thecornea to the depth plane, from the retina to the depth plane, from theeyepiece (e.g., a waveguide of the display device) to the depth plane,and so on.

Without being limited by theory, it is believed that users may stillperceive accommodation-vergence mismatches of up to about 0.25 diopter,up to about 0.33 diopter, and up to about 0.5 diopter as beingphysiologically correct, without the mismatch itself causing significantdiscomfort. In some embodiments, display systems disclosed herein (e.g.,the display system 250, FIG. 6) present images to the viewer havingaccommodation-vergence mismatch of about 0.5 diopter or less. In someother embodiments, the accommodation-vergence mismatch of the imagesprovided by the display system is about 0.33 diopter or less. In yetother embodiments, the accommodation-vergence mismatch of the imagesprovided by the display system is about 0.25 diopter or less, includingabout 0.1 diopter or less.

FIG. 5 illustrates aspects of an approach for simulatingthree-dimensional imagery by modifying wavefront divergence. The displaysystem includes a waveguide 270 that is configured to receive light 770that is encoded with image information, and to output that light to theuser's eye 210. The waveguide 270 may output the light 650 with adefined amount of wavefront divergence corresponding to the wavefrontdivergence of a light field produced by a point on a desired depth plane240. In some embodiments, the same amount of wavefront divergence isprovided for all objects presented on that depth plane. In addition, itwill be illustrated that the other eye of the user may be provided withimage information from a similar waveguide.

In some embodiments, a single waveguide may be configured to outputlight with a set amount of wavefront divergence corresponding to asingle or limited number of depth planes and/or the waveguide may beconfigured to output light of a limited range of wavelengths.Consequently, in some embodiments, a plurality or stack of waveguidesmay be utilized to provide different amounts of wavefront divergence fordifferent depth planes and/or to output light of different ranges ofwavelengths. As used herein, it will be appreciated at a depth plane maybe planar or may follow the contours of a curved surface.

FIG. 6 illustrates an example of a waveguide stack for outputting imageinformation to a user. A display system 250 includes a stack ofwaveguides, or stacked waveguide assembly, 260 that may be utilized toprovide three-dimensional perception to the eye/brain using a pluralityof waveguides 270, 280, 290, 300, 310. It will be appreciated that thedisplay system 250 may be considered a light field display in someembodiments. In addition, the waveguide assembly 260 may also bereferred to as an eyepiece.

In some embodiments, the display system 250 may be configured to providesubstantially continuous cues to vergence and multiple discrete cues toaccommodation. The cues to vergence may be provided by displayingdifferent images to each of the eyes of the user, and the cues toaccommodation may be provided by outputting the light that forms theimages with selectable discrete amounts of wavefront divergence. Statedanother way, the display system 250 may be configured to output lightwith variable levels of wavefront divergence. In some embodiments, eachdiscrete level of wavefront divergence corresponds to a particular depthplane and may be provided by a particular one of the waveguides 270,280, 290, 300, 310.

With continued reference to FIG. 6, the waveguide assembly 260 may alsoinclude a plurality of features 320, 330, 340, 350 between thewaveguides. In some embodiments, the features 320, 330, 340, 350 may beone or more lenses. The waveguides 270, 280, 290, 300, 310 and/or theplurality of lenses 320, 330, 340, 350 may be configured to send imageinformation to the eye with various levels of wavefront curvature orlight ray divergence. Each waveguide level may be associated with aparticular depth plane and may be configured to output image informationcorresponding to that depth plane. Image injection devices 360, 370,380, 390, 400 may function as a source of light for the waveguides andmay be utilized to inject image information into the waveguides 270,280, 290, 300, 310, each of which may be configured, as describedherein, to distribute incoming light across each respective waveguide,for output toward the eye 210. Light exits an output surface 410, 420,430, 440, 450 of the image injection devices 360, 370, 380, 390, 400 andis injected into a corresponding input surface 460, 470, 480, 490, 500of the waveguides 270, 280, 290, 300, 310. In some embodiments, each ofthe input surfaces 460, 470, 480, 490, 500 may be an edge of acorresponding waveguide, or may be part of a major surface of thecorresponding waveguide (that is, one of the waveguide surfaces directlyfacing the world 510 or the viewer's eye 210). In some embodiments, asingle beam of light (e.g. a collimated beam) may be injected into eachwaveguide to output an entire field of cloned collimated beams that aredirected toward the eye 210 at particular angles (and amounts ofdivergence) corresponding to the depth plane associated with aparticular waveguide. In some embodiments, a single one of the imageinjection devices 360, 370, 380, 390, 400 may be associated with andinject light into a plurality (e.g., three) of the waveguides 270, 280,290, 300, 310.

In some embodiments, the image injection devices 360, 370, 380, 390, 400are discrete displays that each produce image information for injectioninto a corresponding waveguide 270, 280, 290, 300, 310, respectively. Insome other embodiments, the image injection devices 360, 370, 380, 390,400 are the output ends of a single multiplexed display which may, e.g.,pipe image information via one or more optical conduits (such as fiberoptic cables) to each of the image injection devices 360, 370, 380, 390,400. It will be appreciated that the image information provided by theimage injection devices 360, 370, 380, 390, 400 may include light ofdifferent wavelengths, or colors (e.g., different component colors, asdiscussed herein).

In some embodiments, the light injected into the waveguides 270, 280,290, 300, 310 is provided by a light projector system 520, whichcomprises a light module 530, which may include a light emitter, such asa light emitting diode (LED). The light from the light module 530 may bedirected to and modified by a light modulator 540, e.g., a spatial lightmodulator, via a beam splitter 550. The light modulator 540 may beconfigured to change the perceived intensity of the light injected intothe waveguides 270, 280, 290, 300, 310 to encode the light with imageinformation. Examples of spatial light modulators include liquid crystaldisplays (LCD) including a liquid crystal on silicon (LCOS) displays. Itwill be appreciated that the image injection devices 360, 370, 380, 390,400 are illustrated schematically and, in some embodiments, these imageinjection devices may represent different light paths and locations in acommon projection system configured to output light into associated onesof the waveguides 270, 280, 290, 300, 310. In some embodiments, thewaveguides of the waveguide assembly 260 may function as ideal lenswhile relaying light injected into the waveguides out to the user'seyes. In this conception, the object may be the spatial light modulator540 and the image may be the image on the depth plane.

In some embodiments, the display system 250 may be a scanning fiberdisplay comprising one or more scanning fibers configured to projectlight in various patterns (e.g., raster scan, spiral scan, Lissajouspatterns, etc.) into one or more waveguides 270, 280, 290, 300, 310 andultimately to the eye 210 of the viewer. In some embodiments, theillustrated image injection devices 360, 370, 380, 390, 400 mayschematically represent a single scanning fiber or a bundle of scanningfibers configured to inject light into one or a plurality of thewaveguides 270, 280, 290, 300, 310. In some other embodiments, theillustrated image injection devices 360, 370, 380, 390, 400 mayschematically represent a plurality of scanning fibers or a plurality ofbundles of scanning fibers, each of which are configured to inject lightinto an associated one of the waveguides 270, 280, 290, 300, 310. Itwill be appreciated that one or more optical fibers may be configured totransmit light from the light module 530 to the one or more waveguides270, 280, 290, 300, 310. It will be appreciated that one or moreintervening optical structures may be provided between the scanningfiber, or fibers, and the one or more waveguides 270, 280, 290, 300, 310to, e.g., redirect light exiting the scanning fiber into the one or morewaveguides 270, 280, 290, 300, 310.

A controller 560 controls the operation of one or more of the stackedwaveguide assembly 260, including operation of the image injectiondevices 360, 370, 380, 390, 400, the light source 530, and the lightmodulator 540. In some embodiments, the controller 560 is part of thelocal data processing module 140. The controller 560 includesprogramming (e.g., instructions in a non-transitory medium) thatregulates the timing and provision of image information to thewaveguides 270, 280, 290, 300, 310 according to, e.g., any of thevarious schemes disclosed herein. In some embodiments, the controllermay be a single integral device, or a distributed system connected bywired or wireless communication channels. The controller 560 may be partof the processing modules 140 or 150 (FIG. 9D) in some embodiments.

With continued reference to FIG. 6, the waveguides 270, 280, 290, 300,310 may be configured to propagate light within each respectivewaveguide by total internal reflection (TIR). The waveguides 270, 280,290, 300, 310 may each be planar or have another shape (e.g., curved),with major top and bottom surfaces and edges extending between thosemajor top and bottom surfaces. In the illustrated configuration, thewaveguides 270, 280, 290, 300, 310 may each include out-coupling opticalelements 570, 580, 590, 600, 610 that are configured to extract lightout of a waveguide by redirecting the light, propagating within eachrespective waveguide, out of the waveguide to output image informationto the eye 210. Extracted light may also be referred to as out-coupledlight and the out-coupling optical elements light may also be referredto light extracting optical elements. An extracted beam of light may beoutputted by the waveguide at locations at which the light propagatingin the waveguide strikes a light extracting optical element. Theout-coupling optical elements 570, 580, 590, 600, 610 may, for example,be gratings, including diffractive optical features, as discussedfurther herein. While illustrated disposed at the bottom major surfacesof the waveguides 270, 280, 290, 300, 310, for ease of description anddrawing clarity, in some embodiments, the out-coupling optical elements570, 580, 590, 600, 610 may be disposed at the top and/or bottom majorsurfaces, and/or may be disposed directly in the volume of thewaveguides 270, 280, 290, 300, 310, as discussed further herein. In someembodiments, the out-coupling optical elements 570, 580, 590, 600, 610may be formed in a layer of material that is attached to a transparentsubstrate to form the waveguides 270, 280, 290, 300, 310. In some otherembodiments, the waveguides 270, 280, 290, 300, 310 may be a monolithicpiece of material and the out-coupling optical elements 570, 580, 590,600, 610 may be formed on a surface and/or in the interior of that pieceof material.

With continued reference to FIG. 6, as discussed herein, each waveguide270, 280, 290, 300, 310 is configured to output light to form an imagecorresponding to a particular depth plane. For example, the waveguide270 nearest the eye may be configured to deliver collimated light (whichwas injected into such waveguide 270), to the eye 210. The collimatedlight may be representative of the optical infinity focal plane. Thenext waveguide up 280 may be configured to send out collimated lightwhich passes through the first lens 350 (e.g., a negative lens) beforeit may reach the eye 210; such first lens 350 may be configured tocreate a slight convex wavefront curvature so that the eye/braininterprets light coming from that next waveguide up 280 as coming from afirst focal plane closer inward toward the eye 210 from opticalinfinity. Similarly, the third up waveguide 290 passes its output lightthrough both the first 350 and second 340 lenses before reaching the eye210; the combined optical power of the first 350 and second 340 lensesmay be configured to create another incremental amount of wavefrontcurvature so that the eye/brain interprets light coming from the thirdwaveguide 290 as coming from a second focal plane that is even closerinward toward the person from optical infinity than was light from thenext waveguide up 280.

The other waveguide layers 300, 310 and lenses 330, 320 are similarlyconfigured, with the highest waveguide 310 in the stack sending itsoutput through all of the lenses between it and the eye for an aggregatefocal power representative of the closest focal plane to the person. Tocompensate for the stack of lenses 320, 330, 340, 350 whenviewing/interpreting light coming from the world 510 on the other sideof the stacked waveguide assembly 260, a compensating lens layer 620 maybe disposed at the top of the stack to compensate for the aggregatepower of the lens stack 320, 330, 340, 350 below. Such a configurationprovides as many perceived focal planes as there are availablewaveguide/lens pairings. Both the out-coupling optical elements of thewaveguides and the focusing aspects of the lenses may be static (i.e.,not dynamic or electro-active). In some alternative embodiments, eitheror both may be dynamic using electro-active features.

In some embodiments, two or more of the waveguides 270, 280, 290, 300,310 may have the same associated depth plane. For example, multiplewaveguides 270, 280, 290, 300, 310 may be configured to output imagesset to the same depth plane, or multiple subsets of the waveguides 270,280, 290, 300, 310 may be configured to output images set to the sameplurality of depth planes, with one set for each depth plane. This mayprovide advantages for forming a tiled image to provide an expandedfield of view at those depth planes.

With continued reference to FIG. 6, the out-coupling optical elements570, 580, 590, 600, 610 may be configured to both redirect light out oftheir respective waveguides and to output this light with theappropriate amount of divergence or collimation for a particular depthplane associated with the waveguide. As a result, waveguides havingdifferent associated depth planes may have different configurations ofout-coupling optical elements 570, 580, 590, 600, 610, which outputlight with a different amount of divergence depending on the associateddepth plane. In some embodiments, the light extracting optical elements570, 580, 590, 600, 610 may be volumetric or surface features, which maybe configured to output light at specific angles. For example, the lightextracting optical elements 570, 580, 590, 600, 610 may be volumeholograms, surface holograms, and/or diffraction gratings. In someembodiments, the features 320, 330, 340, 350 may not be lenses; rather,they may simply be spacers (e.g., cladding layers and/or structures forforming air gaps).

In some embodiments, the out-coupling optical elements 570, 580, 590,600, 610 are diffractive features that form a diffraction pattern, or“diffractive optical element” (also referred to herein as a “DOE”).Preferably, the DOE's have a sufficiently low diffraction efficiency sothat only a portion of the light of the beam is deflected away towardthe eye 210 with each intersection of the DOE, while the rest continuesto move through a waveguide via TIR. The light carrying the imageinformation is thus divided into a number of related exit beams thatexit the waveguide at a multiplicity of locations and the result is afairly uniform pattern of exit emission toward the eye 210 for thisparticular collimated beam bouncing around within a waveguide.

In some embodiments, one or more DOEs may be switchable between “on”states in which they actively diffract, and “off” states in which theydo not significantly diffract. For instance, a switchable DOE maycomprise a layer of polymer dispersed liquid crystal, in whichmicrodroplets comprise a diffraction pattern in a host medium, and therefractive index of the microdroplets may be switched to substantiallymatch the refractive index of the host material (in which case thepattern does not appreciably diffract incident light) or themicrodroplet may be switched to an index that does not match that of thehost medium (in which case the pattern actively diffracts incidentlight).

In some embodiments, a camera assembly 630 (e.g., a digital camera,including visible light and infrared light cameras) may be provided tocapture images of the eye 210 and/or tissue around the eye 210 to, e.g.,detect user inputs and/or to monitor the physiological state of theuser. As used herein, a camera may be any image capture device. In someembodiments, the camera assembly 630 may include an image capture deviceand a light source to project light (e.g., infrared light) to the eye,which may then be reflected by the eye and detected by the image capturedevice. In some embodiments, the camera assembly 630 may be attached tothe frame 80 (FIG. 9D) and may be in electrical communication with theprocessing modules 140 and/or 150, which may process image informationfrom the camera assembly 630. In some embodiments, one camera assembly630 may be utilized for each eye, to separately monitor each eye.

With reference now to FIG. 7, an example of exit beams outputted by awaveguide is shown. One waveguide is illustrated, but it will beappreciated that other waveguides in the waveguide assembly 260 (FIG. 6)may function similarly, where the waveguide assembly 260 includesmultiple waveguides. Light 640 is injected into the waveguide 270 at theinput surface 460 of the waveguide 270 and propagates within thewaveguide 270 by TIR. At points where the light 640 impinges on the DOE570, a portion of the light exits the waveguide as exit beams 650. Theexit beams 650 are illustrated as substantially parallel but, asdiscussed herein, they may also be redirected to propagate to the eye210 at an angle (e.g., forming divergent exit beams), depending on thedepth plane associated with the waveguide 270. It will be appreciatedthat substantially parallel exit beams may be indicative of a waveguidewith out-coupling optical elements that out-couple light to form imagesthat appear to be set on a depth plane at a large distance (e.g.,optical infinity) from the eye 210. Other waveguides or other sets ofout-coupling optical elements may output an exit beam pattern that ismore divergent, which would require the eye 210 to accommodate to acloser distance to bring it into focus on the retina and would beinterpreted by the brain as light from a distance closer to the eye 210than optical infinity.

In some embodiments, a full color image may be formed at each depthplane by overlaying images in each of the component colors, e.g., threeor more component colors. FIG. 8 illustrates an example of a stackedwaveguide assembly in which each depth plane includes images formedusing multiple different component colors. The illustrated embodimentshows depth planes 240 a-240 f, although more or fewer depths are alsocontemplated. Each depth plane may have three or more component colorimages associated with it, including: a first image of a first color, G;a second image of a second color, R; and a third image of a third color,B. Different depth planes are indicated in the figure by differentnumbers for diopters (dpt) following the letters G, R, and B. Just asexamples, the numbers following each of these letters indicate diopters(1/m), or inverse distance of the depth plane from a viewer, and eachbox in the figures represents an individual component color image. Insome embodiments, to account for differences in the eye's focusing oflight of different wavelengths, the exact placement of the depth planesfor different component colors may vary. For example, differentcomponent color images for a given depth plane may be placed on depthplanes corresponding to different distances from the user. Such anarrangement may increase visual acuity and user comfort and/or maydecrease chromatic aberrations.

In some embodiments, light of each component color may be outputted by asingle dedicated waveguide and, consequently, each depth plane may havemultiple waveguides associated with it. In such embodiments, each box inthe figures including the letters G, R, or B may be understood torepresent an individual waveguide, and three waveguides may be providedper depth plane where three component color images are provided perdepth plane. While the waveguides associated with each depth plane areshown adjacent to one another in this drawing for ease of description,it will be appreciated that, in a physical device, the waveguides mayall be arranged in a stack with one waveguide per level. In some otherembodiments, multiple component colors may be outputted by the samewaveguide, such that, e.g., only a single waveguide may be provided perdepth plane.

With continued reference to FIG. 8, in some embodiments, G is the colorgreen, R is the color red, and B is the color blue. In some otherembodiments, other colors associated with other wavelengths of light,including magenta and cyan, may be used in addition to or may replaceone or more of red, green, or blue.

It will be appreciated that references to a given color of lightthroughout this disclosure will be understood to encompass light of oneor more wavelengths within a range of wavelengths of light that areperceived by a viewer as being of that given color. For example, redlight may include light of one or more wavelengths in the range of about620-780 nm, green light may include light of one or more wavelengths inthe range of about 492-577 nm, and blue light may include light of oneor more wavelengths in the range of about 435-493 nm.

In some embodiments, the light source 530 (FIG. 6) may be configured toemit light of one or more wavelengths outside the visual perceptionrange of the viewer, for example, infrared and/or ultravioletwavelengths. In addition, the in-coupling, out-coupling, and other lightredirecting structures of the waveguides of the display 250 may beconfigured to direct and emit this light out of the display towards theuser's eye 210, e.g., for imaging and/or user stimulation applications.

With reference now to FIG. 9A, in some embodiments, light impinging on awaveguide may need to be redirected to in-couple that light into thewaveguide. An in-coupling optical element may be used to redirect andin-couple the light into its corresponding waveguide. FIG. 9Aillustrates a cross-sectional side view of an example of a plurality orset 660 of stacked waveguides that each includes an in-coupling opticalelement. The waveguides may each be configured to output light of one ormore different wavelengths, or one or more different ranges ofwavelengths. It will be appreciated that the stack 660 may correspond tothe stack 260 (FIG. 6) and the illustrated waveguides of the stack 660may correspond to part of the plurality of waveguides 270, 280, 290,300, 310, except that light from one or more of the image injectiondevices 360, 370, 380, 390, 400 is injected into the waveguides from aposition that requires light to be redirected for in-coupling.

The illustrated set 660 of stacked waveguides includes waveguides 670,680, and 690. Each waveguide includes an associated in-coupling opticalelement (which may also be referred to as a light input area on thewaveguide), with, e.g., in-coupling optical element 700 disposed on amajor surface (e.g., an upper major surface) of waveguide 670,in-coupling optical element 710 disposed on a major surface (e.g., anupper major surface) of waveguide 680, and in-coupling optical element720 disposed on a major surface (e.g., an upper major surface) ofwaveguide 690. In some embodiments, one or more of the in-couplingoptical elements 700, 710, 720 may be disposed on the bottom majorsurface of the respective waveguide 670, 680, 690 (particularly wherethe one or more in-coupling optical elements are reflective, deflectingoptical elements). As illustrated, the in-coupling optical elements 700,710, 720 may be disposed on the upper major surface of their respectivewaveguide 670, 680, 690 (or the top of the next lower waveguide),particularly where those in-coupling optical elements are transmissive,deflecting optical elements. In some embodiments, the in-couplingoptical elements 700, 710, 720 may be disposed in the body of therespective waveguide 670, 680, 690. In some embodiments, as discussedherein, the in-coupling optical elements 700, 710, 720 are wavelengthselective, such that they selectively redirect one or more wavelengthsof light, while transmitting other wavelengths of light. Whileillustrated on one side or corner of their respective waveguide 670,680, 690, it will be appreciated that the in-coupling optical elements700, 710, 720 may be disposed in other areas of their respectivewaveguide 670, 680, 690 in some embodiments.

As illustrated, the in-coupling optical elements 700, 710, 720 may belaterally offset from one another. In some embodiments, each in-couplingoptical element may be offset such that it receives light without thatlight passing through another in-coupling optical element. For example,each in-coupling optical element 700, 710, 720 may be configured toreceive light from a different image injection device 360, 370, 380,390, and 400 as shown in FIG. 6, and may be separated (e.g., laterallyspaced apart) from other in-coupling optical elements 700, 710, 720 suchthat it substantially does not receive light from the other ones of thein-coupling optical elements 700, 710, 720.

Each waveguide also includes associated light distributing elements,with, e.g., light distributing elements 730 disposed on a major surface(e.g., a top major surface) of waveguide 670, light distributingelements 740 disposed on a major surface (e.g., a top major surface) ofwaveguide 680, and light distributing elements 750 disposed on a majorsurface (e.g., a top major surface) of waveguide 690. In some otherembodiments, the light distributing elements 730, 740, 750, may bedisposed on a bottom major surface of associated waveguides 670, 680,690, respectively. In some other embodiments, the light distributingelements 730, 740, 750, may be disposed on both top and bottom majorsurface of associated waveguides 670, 680, 690, respectively; or thelight distributing elements 730, 740, 750, may be disposed on differentones of the top and bottom major surfaces in different associatedwaveguides 670, 680, 690, respectively.

The waveguides 670, 680, 690 may be spaced apart and separated by, e.g.,gas, liquid, and/or solid layers of material. For example, asillustrated, layer 760 a may separate waveguides 670 and 680; and layer760 b may separate waveguides 680 and 690. In some embodiments, thelayers 760 a and 760 b are formed of low refractive index materials(that is, materials having a lower refractive index than the materialforming the immediately adjacent one of waveguides 670, 680, 690).Preferably, the refractive index of the material forming the layers 760a, 760 b is 0.05 or more, or 0.10 or less than the refractive index ofthe material forming the waveguides 670, 680, 690. Advantageously, thelower refractive index layers 760 a, 760 b may function as claddinglayers that facilitate total internal reflection (TIR) of light throughthe waveguides 670, 680, 690 (e.g., TIR between the top and bottom majorsurfaces of each waveguide). In some embodiments, the layers 760 a, 760b are formed of air. While not illustrated, it will be appreciated thatthe top and bottom of the illustrated set 660 of waveguides may includeimmediately neighboring cladding layers.

Preferably, for ease of manufacturing and other considerations, thematerial forming the waveguides 670, 680, 690 are similar or the same,and the material forming the layers 760 a, 760 b are similar or thesame. In some embodiments, the material forming the waveguides 670, 680,690 may be different between one or more waveguides, and/or the materialforming the layers 760 a, 760 b may be different, while still holding tothe various refractive index relationships noted above.

With continued reference to FIG. 9A, light rays 770, 780, 790 areincident on the set 660 of waveguides. It will be appreciated that thelight rays 770, 780, 790 may be injected into the waveguides 670, 680,690 by one or more image injection devices 360, 370, 380, 390, 400 (FIG.6).

In some embodiments, the light rays 770, 780, 790 have differentproperties, e.g., different wavelengths or different ranges ofwavelengths, which may correspond to different colors. The in-couplingoptical elements 700, 710, 720 each deflect the incident light such thatthe light propagates through a respective one of the waveguides 670,680, 690 by TIR. In some embodiments, the incoupling optical elements700, 710, 720 each selectively deflect one or more particularwavelengths of light, while transmitting other wavelengths to anunderlying waveguide and associated incoupling optical element.

For example, in-coupling optical element 700 may be configured todeflect ray 770, which has a first wavelength or range of wavelengths,while transmitting rays 780 and 790, which have different second andthird wavelengths or ranges of wavelengths, respectively. Thetransmitted ray 780 impinges on and is deflected by the in-couplingoptical element 710, which is configured to deflect light of a secondwavelength or range of wavelengths. The ray 790 is deflected by thein-coupling optical element 720, which is configured to selectivelydeflect light of third wavelength or range of wavelengths.

With continued reference to FIG. 9A, the deflected light rays 770, 780,790 are deflected so that they propagate through a correspondingwaveguide 670, 680, 690; that is, the in-coupling optical elements 700,710, 720 of each waveguide deflects light into that correspondingwaveguide 670, 680, 690 to in-couple light into that correspondingwaveguide. The light rays 770, 780, 790 are deflected at angles thatcause the light to propagate through the respective waveguide 670, 680,690 by TIR. The light rays 770, 780, 790 propagate through therespective waveguide 670, 680, 690 by TIR until impinging on thewaveguide's corresponding light distributing elements 730, 740, 750.

With reference now to FIG. 9B, a perspective view of an example of theplurality of stacked waveguides of FIG. 9A is illustrated. As notedabove, the in-coupled light rays 770, 780, 790, are deflected by thein-coupling optical elements 700, 710, 720, respectively, and thenpropagate by TIR within the waveguides 670, 680, 690, respectively. Thelight rays 770, 780, 790 then impinge on the light distributing elements730, 740, 750, respectively. The light distributing elements 730, 740,750 deflect the light rays 770, 780, 790 so that they propagate towardsthe out-coupling optical elements 800, 810, 820, respectively.

In some embodiments, the light distributing elements 730, 740, 750 areorthogonal pupil expanders (OPE's). In some embodiments, the OPE'sdeflect or distribute light to the out-coupling optical elements 800,810, 820 and, in some embodiments, may also increase the beam or spotsize of this light as it propagates to the out-coupling opticalelements. In some embodiments, the light distributing elements 730, 740,750 may be omitted and the in-coupling optical elements 700, 710, 720may be configured to deflect light directly to the out-coupling opticalelements 800, 810, 820. For example, with reference to FIG. 9A, thelight distributing elements 730, 740, 750 may be replaced without-coupling optical elements 800, 810, 820, respectively. In someembodiments, the out-coupling optical elements 800, 810, 820 are exitpupils (EP's) or exit pupil expanders (EPE's) that direct light in aviewer's eye 210 (FIG. 7). It will be appreciated that the OPE's may beconfigured to increase the dimensions of the eye box in at least oneaxis and the EPE's may be to increase the eye box in an axis crossing,e.g., orthogonal to, the axis of the OPEs. For example, each OPE may beconfigured to redirect a portion of the light striking the OPE to an EPEof the same waveguide, while allowing the remaining portion of the lightto continue to propagate down the waveguide. Upon impinging on the OPEagain, another portion of the remaining light is redirected to the EPE,and the remaining portion of that portion continues to propagate furtherdown the waveguide, and so on. Similarly, upon striking the EPE, aportion of the impinging light is directed out of the waveguide towardsthe user, and a remaining portion of that light continues to propagatethrough the waveguide until it strikes the EP again, at which timeanother portion of the impinging light is directed out of the waveguide,and so on. Consequently, a single beam of incoupled light may be“replicated” each time a portion of that light is redirected by an OPEor EPE, thereby forming a field of cloned beams of light, as shown inFIG. 6. In some embodiments, the OPE and/or EPE may be configured tomodify a size of the beams of light.

Accordingly, with reference to FIGS. 9A and 9B, in some embodiments, theset 660 of waveguides includes waveguides 670, 680, 690; in-couplingoptical elements 700, 710, 720; light distributing elements (e.g.,OPE's) 730, 740, 750; and out-coupling optical elements (e.g., EP's)800, 810, 820 for each component color. The waveguides 670, 680, 690 maybe stacked with an air gap/cladding layer between each one. Thein-coupling optical elements 700, 710, 720 redirect or deflect incidentlight (with different in-coupling optical elements receiving light ofdifferent wavelengths) into its waveguide. The light then propagates atan angle which will result in TIR within the respective waveguide 670,680, 690. In the example shown, light ray 770 (e.g., blue light) isdeflected by the first in-coupling optical element 700, and thencontinues to bounce down the waveguide, interacting with the lightdistributing element (e.g., OPE's) 730 and then the out-coupling opticalelement (e.g., EPs) 800, in a manner described earlier. The light rays780 and 790 (e.g., green and red light, respectively) will pass throughthe waveguide 670, with light ray 780 impinging on and being deflectedby in-coupling optical element 710. The light ray 780 then bounces downthe waveguide 680 via TIR, proceeding on to its light distributingelement (e.g., OPEs) 740 and then the out-coupling optical element(e.g., EP's) 810. Finally, light ray 790 (e.g., red light) passesthrough the waveguide 690 to impinge on the light in-coupling opticalelements 720 of the waveguide 690. The light in-coupling opticalelements 720 deflect the light ray 790 such that the light raypropagates to light distributing element (e.g., OPEs) 750 by TIR, andthen to the out-coupling optical element (e.g., EPs) 820 by TIR. Theout-coupling optical element 820 then finally out-couples the light ray790 to the viewer, who also receives the out-coupled light from theother waveguides 670, 680.

FIG. 9C illustrates a top-down plan view of an example of the pluralityof stacked waveguides of FIGS. 9A and 9B. As illustrated, the waveguides670, 680, 690, along with each waveguide's associated light distributingelement 730, 740, 750 and associated out-coupling optical element 800,810, 820, may be vertically aligned. However, as discussed herein, thein-coupling optical elements 700, 710, 720 are not vertically aligned;rather, the in-coupling optical elements are preferably non-overlapping(e.g., laterally spaced apart as seen in the top-down view). Asdiscussed further herein, this nonoverlapping spatial arrangementfacilitates the injection of light from different resources intodifferent waveguides on a one-to-one basis, thereby allowing a specificlight source to be uniquely coupled to a specific waveguide. In someembodiments, arrangements including nonoverlapping spatially-separatedin-coupling optical elements may be referred to as a shifted pupilsystem, and the in-coupling optical elements within these arrangementsmay correspond to sub pupils.

FIG. 9D illustrates an example of wearable display system 60 into whichthe various waveguides and related systems disclosed herein may beintegrated. In some embodiments, the display system 60 is the system 250of FIG. 6, with FIG. 6 schematically showing some parts of that system60 in greater detail. For example, the waveguide assembly 260 of FIG. 6may be part of the display 70.

With continued reference to FIG. 9D, the display system 60 includes adisplay 70, and various mechanical and electronic modules and systems tosupport the functioning of that display 70. The display 70 may becoupled to a frame 80, which is wearable by a display system user orviewer 90 and which is configured to position the display 70 in front ofthe eyes of the user 90. The display 70 may be considered eyewear insome embodiments. In some embodiments, a speaker 100 is coupled to theframe 80 and configured to be positioned adjacent the ear canal of theuser 90 (in some embodiments, another speaker, not shown, may optionallybe positioned adjacent the other ear canal of the user to providestereo/shapeable sound control). The display system 60 may also includeone or more microphones 110 or other devices to detect sound. In someembodiments, the microphone is configured to allow the user to provideinputs or commands to the system 60 (e.g., the selection of voice menucommands, natural language questions, etc.), and/or may allow audiocommunication with other persons (e.g., with other users of similardisplay systems. The microphone may further be configured as aperipheral sensor to collect audio data (e.g., sounds from the userand/or environment). In some embodiments, the display system may alsoinclude a peripheral sensor 120 a, which may be separate from the frame80 and attached to the body of the user 90 (e.g., on the head, torso, anextremity, etc. of the user 90). The peripheral sensor 120 a may beconfigured to acquire data characterizing a physiological state of theuser 90 in some embodiments. For example, the sensor 120 a may be anelectrode.

With continued reference to FIG. 9D, the display 70 is operativelycoupled by communications link 130, such as by a wired lead or wirelessconnectivity, to a local data processing module 140 which may be mountedin a variety of configurations, such as fixedly attached to the frame80, fixedly attached to a helmet or hat worn by the user, embedded inheadphones, or otherwise removably attached to the user 90 (e.g., in abackpack-style configuration, in a belt-coupling style configuration).Similarly, the sensor 120 a may be operatively coupled by communicationslink 120 b, e.g., a wired lead or wireless connectivity, to the localprocessor and data module 140. The local processing and data module 140may comprise a hardware processor, as well as digital memory, such asnon-volatile memory (e.g., flash memory or hard disk drives), both ofwhich may be utilized to assist in the processing, caching, and storageof data. Optionally, the local processor and data module 140 may includeone or more central processing units (CPUs), graphics processing units(GPUs), dedicated processing hardware, and so on. The data may includedata a) captured from sensors (which may be, e.g., operatively coupledto the frame 80 or otherwise attached to the user 90), such as imagecapture devices (such as cameras), microphones, inertial measurementunits, accelerometers, compasses, GPS units, radio devices, gyros,and/or other sensors disclosed herein; and/or b) acquired and/orprocessed using remote processing module 150 and/or remote datarepository 160 (including data relating to virtual content), possiblyfor passage to the display 70 after such processing or retrieval. Thelocal processing and data module 140 may be operatively coupled bycommunication links 170, 180, such as via a wired or wirelesscommunication links, to the remote processing module 150 and remote datarepository 160 such that these remote modules 150, 160 are operativelycoupled to each other and available as resources to the local processingand data module 140. In some embodiments, the local processing and datamodule 140 may include one or more of the image capture devices,microphones, inertial measurement units, accelerometers, compasses, GPSunits, radio devices, and/or gyros. In some other embodiments, one ormore of these sensors may be attached to the frame 80, or may bestandalone structures that communicate with the local processing anddata module 140 by wired or wireless communication pathways.

With continued reference to FIG. 9D, in some embodiments, the remoteprocessing module 150 may comprise one or more processors configured toanalyze and process data and/or image information, for instanceincluding one or more central processing units (CPUs), graphicsprocessing units (GPUs), dedicated processing hardware, and so on. Insome embodiments, the remote data repository 160 may comprise a digitaldata storage facility, which may be available through the internet orother networking configuration in a “cloud” resource configuration. Insome embodiments, the remote data repository 160 may include one or moreremote servers, which provide information, e.g., information forgenerating augmented reality content, to the local processing and datamodule 140 and/or the remote processing module 150. In some embodiments,all data is stored and all computations are performed in the localprocessing and data module, allowing fully autonomous use from a remotemodule. Optionally, an outside system (e.g., a system of one or moreprocessors, one or more computers) that includes CPUs, GPUs, and so on,may perform at least a portion of processing (e.g., generating imageinformation, processing data) and provide information to, and receiveinformation from, modules 140, 150, 160, for instance via wireless orwired connections.

Liquid Crystal Materials for Broadband Adaptive Waveplate LensAssemblies

Generally, liquid crystals possess physical properties that may beintermediate between conventional fluids and solids. While liquidcrystals are fluid-like in some aspects, unlike most fluids, thearrangement of molecules within liquid crystals exhibits some structuralorder. Different types of liquid crystals include thermotropic,lyotropic, and polymeric liquid crystals. Thermotropic liquid crystalsdisclosed herein can be implemented in various physical states, e.g.,phases, including a nematic state/phase, a smectic state/phase, a chiralnematic state/phase or a chiral smectic state/phase.

As described herein, liquid crystals in a nematic state or phase canhave calamitic (rod-shaped) or discotic (disc-shaped) organic moleculesthat have relatively little positional order, while having a long-rangedirectional order with their long axes being roughly parallel. Thus, theorganic molecules may be free to flow with their center of masspositions being randomly distributed as in a liquid, while stillmaintaining their long-range directional order. In some implementations,liquid crystals in a nematic phase can be uniaxial; i.e., the liquidcrystals have one axis that is longer and preferred, with the other twobeing roughly equivalent. In some implementations, the liquid crystalmolecules orient their long axis. In other implementations, liquidcrystals can be biaxial; i.e., in addition to orienting their long axis,the liquid crystals may also orient along a secondary axis.

As described herein, liquid crystals in a smectic state or phase canhave the organic molecules that form relatively well-defined layers thatcan slide over one another. In some implementations, liquid crystals ina smectic phase can be positionally ordered along one direction. In someimplementations, the long axes of the molecules can be oriented along adirection substantially normal to the plane of the liquid crystal layer,while in other implementations, the long axes of the molecules may betilted with respect to the direction normal to the plane of the layer.

Herein and throughout the disclosure, nematic liquid crystals arecomposed of rod-like molecules with the long axes of neighboringmolecules approximately aligned to one another. To describe thisanisotropic structure, a dimensionless unit vector n called thedirector, may be used to describe the direction of preferred orientationof the liquid crystal molecules.

Herein and throughout the disclosure, an azimuthal angle or a rotationangle φ is used to describe an angle of rotation of a liquid crystalmolecule about a layer normal direction, or an axis normal to a majorsurface of a liquid crystal layer, which is measured in a plane parallelto a major surface of the liquid crystal layers or of the substrate,e.g., the x-y plane, and measured between an alignment direction, e.g.,an elongation direction or the direction of the director, and adirection parallel to the major surface, e.g., the y-direction.

Herein and throughout the disclosure, when an angle such as the rotationangle φ referred to as being substantially the same or different betweendifferent regions, it will be understood that the average angles can,for example, be within about 1%, about 5% or about 10% of each otheralthough the average angles can be larger in some cases.

As describe herein, some liquid crystals in a nematic state or a smecticstate can also exhibit a twist in a layer normal direction. Such liquidcrystals are referred to as being twisted nematic (TN) liquid crystalsor twisted smectic (SN) liquid crystals. TN or SN liquid crystals canexhibit a twisting of the molecules about an axis perpendicular to thedirector, with the molecular axis being parallel to the director. Whenthe degree of twist is relatively large, twisted liquid crystals may bereferred to as being in a chiral phase or a cholesteric phase.

As described herein, TN or SN liquid crystals can be described as havinga twist angle or a net twist angle (φ), which can refer to, for example,the relative azimuthal angular rotation between an uppermost liquidcrystal molecule and a lowermost liquid crystal molecule across aspecified length, e.g., the thickness of the liquid crystal layer.

As described herein, “polymerizable liquid crystals” may refer to liquidcrystal materials that can be polymerized, e.g., in-situphotopolymerized, and may also be described herein as reactive mesogens(RM).

The liquid crystal molecules may be polymerizable in some embodimentsand, once polymerized, may form a large network with other liquidcrystal molecules. For example, the liquid crystal molecules may belinked by chemical bonds or linking chemical species to other liquidcrystal molecules. Once joined together, the liquid crystal moleculesmay form liquid crystal domains having substantially the sameorientations and locations as before being linked together. The term“liquid crystal molecule” may refer to both the liquid crystal moleculesbefore polymerization and to the liquid crystal domains formed by thesemolecules after polymerization. Once polymerized, the polymerizednetwork may be referred to as liquid crystal polymer (LCP).

In some embodiments, unpolymerized liquid crystal molecules orpolymerizable liquid crystal molecules prior to being polymerized mayhave at least limited rotational degree of freedom. These unpolymerizedliquid crystal molecules can rotate or tilt, e.g., under an electricalstimulus, which results in alteration of the optical properties. Forexample, by applying an electric field, some liquid crystal layersincluding unpolymerized liquid crystal molecules may be switched betweenone or more states having different diffractive or polarization alteringproperties.

The inventors have recognized that the above-described properties ofliquid crystals or reactive mesogens (RMs) can be advantageously appliedto various components of broadband switchable waveplates and waveplatelenses disclosed herein. For example, in some unpolymerized RMs, theorientations of LC molecules of can be altered after deposition, e.g.,by application of an external stimulus, e.g., electric field. Based onthis recognition, the inventors disclose herein waveplates and waveplatelenses that can be switched between a plurality of states by applicationof an external stimulus.

In addition, the inventors have recognized that, when unpolymerized, theorientations of LC molecules at surfaces or interfaces of some LCs orRMs can be aligned by controlling the surface or interface on which theLC molecules are formed. For example, a stack of multiple LC layers canbe formed where, by controlling orientations of LC molecules closest tothe surface of an LC layer, orientations of immediately adjacent LCmolecules in the next LC layer can be controlled, e.g., to have the sameorientation as the LC molecules closest to the surface in the previousLC layer or same orientation as elongated microstructures in adjacentlayers. In addition, LC molecules between the LC molecules at surfacesor interfaces can be controlled to have a predetermined amount of twist.Based on recognition of these and other attributes includingbirefringence, chirality, and ease for multiple-coating, the inventorsdisclose herein waveplates and waveplate lenses that have usefulproperties such as broadband capability with tailored opticalproperties, e.g., diffraction efficiency, optical power andpolarizability, to name a few.

Display Devices Having Switchable Broadband Adaptive Waveplate LensAssemblies

As described supra in reference to FIG. 6, some display systemsaccording to embodiments include a waveguide assembly 260 configured toform images at a plurality of virtual depth planes. The waveguideassembly 260 includes waveguides 270, 280, 290, 300, 310 each configuredto propagate light by total internal reflection (TIR), and includesout-coupling optical elements 570, 580, 590, 600, 610 each configured toextract light out of a respective one of the waveguides 270, 280, 290,300, 310 by redirecting the light. Each of the waveguide 270, 280, 290,300, 310 is configured to output light to form an image corresponding toa particular depth plane. The waveguide assembly 260 may also optionallyinclude a plurality of lenses 320, 330, 340, 350 between the waveguidesfor providing different optical powers for forming the images atdifferent virtual depth planes.

In the illustrated embodiment of the waveguide assembly 260 in FIG. 6,the number of depth planes may be directly proportional to the number ofwaveguides and lenses. However, the inventors have recognized variouschallenges associated with implementing a waveguide assembly configuredfor displaying images at a plurality of depth planes by having aproportional number of waveguides and lenses. For example, a high numberof waveguides 270, 280, 290, 300, 310 and a high number of correspondinglenses 320, 330, 340, 350 can undesirably increase the overallthickness, weight, cost, and manufacturing challenges to the waveguideassembly 260. For example, when formed of a conventional lens material,e.g., glass, each of the lenses 320, 330, 340, 350 may add millimetersor tens of millimeters in thickness and corresponding weight to thedisplays. In addition, a high number of waveguides and lenses canproduce undesirable optical effects to the user, e.g., relatively highabsorption loss. Thus, in one aspect, the inventors have recognized apotential benefit in some cases for display systems that can generateimages at a plurality of depth planes with fewer numbers of waveguides,fewer number of lenses, thinner and lighter waveguides and lenses and/orfewer numbers of lenses per waveguide.

Still referring to FIG. 6, it will be appreciated that the lenses 320,330, 340, 350 may be configured to form images at different depth planesby exerting respective optical powers to light from the waveguides 310,300, 290 and 280. In various embodiments, the light outcoupled from thewaveguides may have a polarization, e.g., a circular polarization.However, when polarized light outcoupled from a waveguide passes througha waveplate lens or a waveplate formed of liquid crystals, less than100% of the outcoupled light transmitted therethrough may be opticallyaffected, e.g., diffractively diverged, converged or altered inpolarization, resulting in a portion of the outcoupled light passingthrough without being optically affected. The light passing through thelens without being optically affected in this manner is sometimesreferred to as leakage light. The leakage light may be undesirablyfocused, defocused or altered in polarization in the downstream opticalpath, or not be affected at all. When a significant portion of the lightpassing through a waveplate or waveplate lens constitutes leakage light,a user may experience undesirable effects, such as, “ghost” images,which are unintended images or images that become visible to the user atunintended depth planes. The inventors have recognized that such leakagelight may result from, among other causes, the waveplate lenses orwaveplates formed of liquid crystals being configured to have arelatively high diffraction efficiency within a relatively narrow rangeof wavelengths in the visible spectrum. Thus, in another aspect, theinventors have recognized a need for a broadband adaptive waveplate lensassembly that can generate images at a plurality of depth planes withless undesirable effects arising from leakage light over a wide range ofwavelengths in the visible spectrum. To address these and other needs,various embodiments include broadband adaptive waveplate lens assembliescomprising switchable waveplate lenses or switchable waveplates based onliquid crystals, which are configured to provide variable optical power.The waveplate lenses and waveplates formed of liquid crystals canprovide various advantages towards achieving these objectives, includingsmall thickness, light weight and high degree of configurability at themolecular level. In various embodiments described herein, displaydevices are configured to form images at different virtual depth planesusing a waveguide assembly configured to guide light in a lateraldirection parallel to an output surface of a waveguide and to outcouplethe guided light through the output surface to one or more broadbandadaptive waveplate lens assemblies. In various embodiments, a broadbandadaptive waveplate lens assembly is configured to incouple and todiffract therethrough the outcoupled light from the waveguide. Thebroadband adaptive lens assembly includes a first waveplate lenscomprising a liquid crystal (LC) layer arranged such that the waveplatelens has birefringence (Δn) that varies in a radially outward directionfrom a central region of the first waveplate lens is configured todiffract the outcoupled light at a diffraction efficiency greater than90%, greater than 95% or even greater than 99% within a broadbandwavelength range including at least 450 nm to 630 nm. In someembodiments, the broadband adaptive waveplate lens assemblies accordingto embodiments are significantly lighter and thinner (microns) comparedto conventional lenses, and can advantageously provide variable opticalpower over a broadband wavelength range. Advantageously, such broadbandadaptive lens assemblies may reduce the number, thickness and weight ofa waveguide assembly such as the waveguide assembly 260 (FIG. 6), aswell as reducing or eliminating undesirable effects arising from leakagelight.

As used herein, optical power (P, also referred to as refractive power,focusing power, or convergence power) refers to the degree to which alens, mirror, or other optical system converges or diverges light. It isequal to the reciprocal of the focal length of the device: P=1/f. Thatis, high optical power corresponds to short focal length. The SI unitfor optical power is the inverse meter (m⁻¹), which is commonly calledthe diopter (D).

As described herein, converging lenses that focus light passingtherethrough are described as having a positive optical power, whilediverging lenses that defocus light passing therethrough are describedas having a negative power. Without being bound by theory, when lightpasses through two or more thin lenses that are relatively close to eachother, the optical power of the combined lenses may be approximated as asum of the optical powers of the individual lenses. Thus, when lightpasses through a first lens having a first optical power P1 and furtherpasses through a second lens having a second optical power P2, the lightmay be understood to converge or diverge according to a sum of opticalpowers Pnet=P1+P2.

A medium having a refractive index that depends on the polarization andpropagation direction of light is referred to be birefringent (orbirefractive). As described throughout the specification and understoodin the relevant industry, light whose polarization is perpendicular tothe optic axis of a birefringent medium is described as having anordinary refractive index (n_(o)), light whose polarization is parallelto the optic axis of the birefringent medium is described as having anextraordinary refractive index (n_(e)), and a difference of therefractive indices n_(e)−n_(o) observed in the birefringent mediummaterial is described as having a birefringence Δn. The phaseretardation of light in a material medium having birefringence Δn can beexpressed as Γ=2πΔnd/λ, at different λ, where d is the thickness of themedium.

Generally, optically anisotropic materials, e.g., liquid crystals,display a positive dispersion of birefringence (Δn) decreasing with alonger wavelength of light λ. The positive dispersion of Δn results indifferent phase retardation Γ=2πΔnd/λ at different λ, where d is thethickness of the medium. As disclosed herein, an anisotropic materialdisplaying a negative dispersion of birefringence (Δn) refers to amaterial in which the birefringence increases with a longer wavelengthof light λ.

As described above, the wavelength dependence of diffraction efficiencyof a waveplate lens or a waveplate can be an important consideration inreducing or minimizing various undesirable optical effects. As describedherein, diffraction efficiency (η) of a birefringent medium such as alayer of liquid crystals can be expressed as η=sin²(πΔnd/λ), where Δn isbirefringence, λ is wavelength and d is the thickness. Because phaseretardation that light propagating through the diffractive componentsvaries with the wavelength for conventional birefringent media, somediffractive components including waveplate lenses and waveplates show arelatively narrow range of wavelengths, or bandwidth, within the visiblespectrum in which diffraction efficiency is sufficiently high. Incontrast, waveplate lenses and waveplates according to embodimentsdisplay a relatively wide range of wavelengths, or bandwidth, within thevisible spectrum in which diffraction efficiency is sufficiently highfor various applications described herein.

According to various embodiments, a broadband waveplate lens or awaveplate may be described as having a normalized bandwidth (Δλ/λ₀),where λ₀ is a center wavelength within the visible spectrum spanning awavelength range of about 400-800 nm, including one or more of a redspectrum having a wavelength range of about 620-780 nm, a green spectrumhaving a wavelength range of about 492-577 nm and a blue spectrum havinga wavelength range of about 435-493 nm, and Δλ is a range of wavelengthscentered about the λ₀ within which a diffraction efficiency exceeds 70%,80%, 90%, 95%, 99% or by any value within a range defined by thesevalues.

According to various embodiments, when a waveplate lens or a waveplateis described as being a broadband waveplate lens or a broadbandwaveplate, it will be understood as having an average, an instantaneous,a mean, a median or a minimum value of diffraction efficiency whichexceeds 70%, 80%, 90%, 95%, 99% or a percentage within any of thesevalues, within at least a portion of a visible spectrum spanning awavelength range of about 400-800 nm, including one or more of a redspectrum which includes wavelengths in the range of about 620-780 nm, agreen spectrum which includes wavelengths in the range of about 492-577nm, and a blue spectrum in the range of about 435-493 nm, or within arange of wavelengths defined by any wavelength within the visiblespectrum within about 400-800 nm, e.g., 400-700 nm, 430-650 nm or450-630 nm.

Based on the relationship η=sin²(πΔnd/λ) described above for diffractionefficiency, a broadband waveplate lens or a waveplate can have anefficiency for a fixed d when the ratio of Δn/λ has a positive andrelatively constant value. As described herein, a medium having apositive ratio value of Δn/λ is referred to as a having a negativedispersion. According to embodiments, broadband waveplate lenses orbroadband waveplates described herein have negative dispersion, or abirefringence (Δn) that increases with increasing wavelength (λ) withinwavelength ranges described above.

According to various embodiments, a broadband waveplate lens or awaveplate may be described as having an instantaneous, a mean, a median,a minimum or a maximum value of the ratio Δn/λ, that is a positive valuewithin any range of the visible spectrum described above. In addition, abroadband waveplate lens or the waveplate has a relatively high ratio ofΔλ/λ₀, where Δλ, is a wavelength range within any range of the visiblespectrum described above and λ₀ is a centroid wavelength within the Δλ.According to various embodiments, a high normalized bandwidth Δλ/λ₀ canhave a value of about 0.3-1.0, 0.3-0.7, 0.4-0.7, 0.5-0.7, 0.6-0.7 or avalue within any range defined by these values. In addition, thebroadband waveplate lens or the waveplate has a ratio Δn/λ, that isrelatively constant within various wavelength ranges within the visiblespectrum described above. For example, the ratio Δn/λ can have adeviation, e.g., a standard deviation, from a mean, a median, a minimumor a maximum value of the ratio Δn/λ that does not exceed more than 30%,20%, 10%, 5%, 1% or a percentage within any of these values.

As described herein, a “transmissive” or “transparent” structure, e.g.,a transparent substrate, may allow at least some, e.g., at least 20, 30,50, 70 or 90%, of an incident light, to pass therethrough. Accordingly,a transparent substrate may be a glass, sapphire or a polymericsubstrate in some embodiments. In contrast, a “reflective” structure,e.g., a reflective substrate, may reflect at least some, e.g., at least20, 30, 50, 70, 90% or more of the incident light, to reflect therefrom.

FIG. 10 illustrates an example of a display device 1000, e.g., awearable display device, comprising one or more broadband adaptive lensassemblies, e.g., a pair of broadband adaptive lens assemblies 1004,1008 in an optical path 1016 that are interposed by a waveguide assembly1012. As described supra, the waveguide assembly includes a waveguideconfigured to propagate light (e.g., visible light) under total internalreflection and to outcouple the light in an optical axis extending from(e.g., in a direction normal to) a light output surface of the waveguide(e.g., a major surface of the waveguide). The light may be outcoupled bya diffraction grating in some embodiments. Each of the broadbandadaptive lens assemblies 1004, 1008 may be configured to at leastpartially transmit outcoupled light therethrough. In the illustratedembodiments, each of the adaptive lens assemblies may be configured toreceive outcoupled light from the waveguide assembly 1012 and toconverge or diverge the outcoupled light in the optical axis direction.Each of the broadband adaptive lens assemblies 1004, 1008 comprises awaveplate lens comprising liquid crystals arranged such that thewaveplate lens has birefringence (Δn) that varies in a radial directionfrom a central region of the waveplate lens and that decreases withincreasing wavelength (λ) within a range of the visible spectrum. Thebroadband adaptive lens assembly is configured to be selectivelyswitched between a plurality of states having different optical powers.The broadband adaptive lens assembly are be configured to alter apolarization state of the outcoupled light passing therethrough whenactivated (e.g., electrically activated).

As used herein, an adaptive lens assembly refers to a lens assemblyhaving at least one optical property that may be adjusted, e.g.,reversibly activated and deactivated, using an external stimulus.Example optical properties that may be reversibly activated anddeactivated include, among other properties, optical power (focallength), phase, polarization, polarization-selectivity, transmissivity,reflectivity, birefringence and diffraction properties, among otherproperties. In various embodiments, adaptive lens assemblies are capableof electrically varying the optical power and the polarization state oflight passing therethrough.

In the illustrated embodiment, each of the pair of broadband adaptivelens assemblies 1004, 1008 is configured to be selectively switchedbetween at least two states, where, in a first state each is configuredto pass the outcoupled light therethrough without altering apolarization state thereof, while in a second state each is configuredto alter the polarization state of the outcoupled light passingtherethrough. For example, in the second state, each of the broadbandadaptive lens assemblies 1004, 1008 reverses the handedness ofcircularly polarized light, while in the first state, each of thebroadband adaptive lens assemblies 1004, 1008 preserves the handednessof circularly polarized light.

Still referring to FIG. 10, the display device 1000 further comprises awaveguide assembly 1012 interposed between the pair of adaptive lensassemblies 1004, 1008. The waveguide assembly 1012 may be similar to thewaveguide assembly 260 described above with respect to FIG. 6, whichcomprises one or more waveguides, similar to one or more waveguides 270,280, 290, 300, 310 in FIG. 6. As described supra, e.g., with respect toFIGS. 6 and 7, the waveguide may be configured to propagate light undertotal internal reflection in a lateral direction parallel to a majorsurface of the waveguide. The waveguide may further be configured tooutcouple the light, e.g., in a direction normal to the major surface ofthe waveguide.

Still referring to FIG. 10, a first adaptive lens assembly 1004 of thepair of adaptive lens assemblies is disposed on a first side of thewaveguide assembly 1012, e.g., the side of the world 510 observed by auser, and a second adaptive lens assembly 1008 of the pair of lensassemblies is disposed on a second side of the waveguide assembly 1012,e.g., the side of the eye 210 of the user. As described infra, the pairof adaptive lens assemblies as configured provides to a user virtualcontent from the waveguide assembly 1012 at a plurality of virtual depthplanes, as well the view of the real world. In some embodiments, thereis little or no distortion due to the presence of the adaptive lensassemblies. The virtual content and the view of the real world areprovided to the user upon activation of the first and second adaptivelens assemblies 1004, 1008, as described infra with respect to FIGS. 11Aand 11B.

FIGS. 11A and 11B illustrate examples of display devices 1100A/1100B,each comprising adaptive lens assemblies in operation to output imageinformation to a user. The display devices 1100A and 1100B in unpoweredstate are structurally identical. The display device 1100A is usedherein to describe outputting virtual image to the user, while thedisplay device 1100B is used herein to describe transmitting a realworld image through the display device 1100B to the user. The displaydevice 1100A/1100B includes a pair of the switchable lenses assemblies1004, 1008 that are configured to be electrically activated by, e.g.,application of a voltage or a current. In some embodiments, in adeactivated state, e.g., when no voltage or current is applied, each ofthe first and second switchable lenses assemblies 1004, 1008 has a low,e.g., about zero, optical power. In some embodiments, in an activatedstate, e.g., when a voltage or a current is applied, the first adaptivelens assembly 1004 on the side of the world may provide a first netoptical power (Pnet1) having a first sign, e.g., a positive opticalpower. When in an activated state, the second adaptive lens assembly1008 on the side of the user may provide a second net optical power(Pnet2) having a second sign, e.g., a negative optical power.

FIG. 11A illustrates an example of the display system of FIG. 10displaying virtual content to a user at a virtual depth plane, accordingto some embodiments. As described supra, the waveguide assembly 1012interposed between the pair of the adaptive lens assemblies 1004, 1008comprises a waveguide configured to receive light containing virtualimage information and propagate the light under total internalreflection. The waveguide assembly 1012 is further configured tooutcouple the light through, e.g., a diffraction grating, towards theeye 210. The outcoupled light passes through the second adaptive lensassembly 1008 prior to entering the eye 210. When activated, the secondadaptive lens assembly 1008 has a second net optical power, Pnet2, whichmay have a negative value, such that the user sees the virtual image ata virtual depth plane 1104.

In some embodiments, the second net optical power Pnet2 may be adjustedelectrically to adjust the second net optical power (Pnet2) of thesecond adaptive lens assembly 1008, thereby adjusting the distance tothe virtual depth plane 1104. For example, as a virtual object “moves”closer and further relative to the eye 210 within a virtual threedimensional space, the second net optical power Pnet2 of the secondadaptive lens assembly 1008 may be correspondingly adjusted, such thatthe virtual depth plane one 1104 adjusts to track the virtual object.Thus, the user may experience relatively little or noaccommodation/vergence mismatch beyond an acceptable threshold. In someembodiments, the magnitude of the distance to the virtual depth plane1104 may be adjusted in discrete steps, while in some other embodiments,the magnitude of the distance to the virtual depth plane 1104 may beadjusted continuously.

FIG. 11B illustrates an example of the display system of FIG. 10providing a view of real world content to a user, according to someembodiments. When the second adaptive lens assembly 1008 is activated tohave the second net optical power (Pnet2) to display the virtual contentat the virtual depth plane 1104, light from the real world passingthrough the second adaptive lens assembly 1008 may also be converged ordiverged according to Pnet2 of the activated second adaptive lensassembly 1008. Thus, objects in the real world may appear out of focus.To mitigate such distortion, according to embodiments, when activated,the first and second adaptive lens assemblies 1004, 1008 may beconfigured to have optical powers having opposite signs. In someembodiments, light passing through the first and second adaptive lensassemblies 1004, 1008 converges or diverges according to a combinedoptical power having a magnitude that is about a difference betweenmagnitudes of first and second net optical powers Pnet1, Pnet2, of thefirst and second adaptive lens assemblies 1004, 1008, respectively. Insome embodiments, the waveguide assembly 1012 may also have opticalpower and the adaptive lens assembly 1008 may be configured to accountfor the distortions caused by both the lens assembly 1004 and thewaveguide assembly 1012. For example, the optical power of the adaptivelens assembly 1008 may be opposite in sign to the sum of the opticalpowers of the lens assembly 1004 and the waveguide assembly 1012.

In some embodiments, the first adaptive lens assembly 1004 is configuredto have the first net optical power Pnet1 that has a magnitude that isclose to or the same as the magnitude of the second net optical powerPnet2 of the second adaptive lens assembly 1008. As a result, when boththe first and second adaptive lens assemblies 1004, 1008 are activatedsimultaneously, objects in the real world appear relatively unaffectedby the optical power of the second adaptive lens assembly 1008 providedfor displaying the virtual content.

In some embodiments, first adaptive lens assembly 1004 may be configuredsuch that when activated, the first net optical power Pnet1 dynamicallymatches the second net optical power Pnet2 of the second adaptive lensassembly 1008. For example, as the second net optical power Pnet1 of thesecond switchable assembly 1008 is adjusted to track moving virtualobjects within the virtual three dimensional space, the first netoptical power Pnet1 of the first adaptive lens assembly 1004 may bedynamically adjusted, such that the magnitude of the combined opticalpower P=Pnet1+Pnet2 may be kept less than a predetermined value. Thus,according to embodiments, the objects in the real world may be preventedfrom being unacceptably out of focus by compensating the second netoptical power (Pnet2) of the second adaptive lens assembly 1008, whichmay have a negative value, with the first net optical power (Pnet1) ofthe first adaptive lens assembly 1004, such that the combined opticalpower P=Pnet1+Pnet2 remains small, e.g., near about 0 m⁻¹.

Switchable Waveplate and Switchable Waveplate Lenses for BroadbandAdaptive Waveplate Lens Assemblies

As discussed above, one of the advantages of forming images at aplurality of depth planes with fewer waveguides is the overall reductionin thickness and weight of the display device (e.g., display device 1000in FIG. 10). Thus, various embodiments described herein provide adaptivewaveplate lens assemblies that are compact, lightweight and providevarious optical functionalities, e.g., high bandwidth capability andvariable optical power. In addition, various embodiments describedherein provide adaptive lens assemblies with relatively low amount ofleakage light.

To provide images at a plurality of depth planes with high efficiencyover a wide range of the visible spectrum, the broadband adaptive lensassembly according to various embodiments include a waveplate lens(1154A, 1154B in FIGS. 12A, 12B, respectively) comprising liquidcrystals arranged such that the waveplate lens has birefringence (Δn)that varies in a radial direction from a central region of the firstwaveplate lens and that decreases with increasing wavelength (λ) withina range of the visible spectrum. As described above, according tovarious embodiments, the broadband adaptive waveplate lens assembly cangenerate images at multiple depth planes by being configured to beselectively switched between a plurality of states with differentoptical powers. The selective switching of the broadband lens assemblycan in turn be performed by switching a waveplate lens or a waveplateincluded in the broadband adaptive wavelplate lens assembly according toembodiments, as discussed herein.

Referring to FIG. 12A, in some embodiments, the broadband adaptive lensassembly 1150A is configured to be switched between different opticalpower states by employing a switchable waveplate 1158 comprising liquidcrystals in the same optical path as the waveplate lens 1154A. Thewaveplate lens 1154A may be a passive lens and the broadband adaptivelens assembly 1150A may be selectively switched between different statesby electrically activating and deactivating the switchable waveplate1158.

Still referring to FIG. 12A, in operation, the waveplate lens 1154A isconfigured such that it diverges or converges incident light 1162A,1162B passing therethrough depending on the polarization of the light,e.g., circular polarization, according to various embodiments. Whenconfigured as a half-waveplate (HWP) lens, the illustrated waveplatelens 1154A, which may be a passive waveplate lens, is configured toconverge a right-hand circular polarized (RHCP) light beam 1162Bincident on the waveplate lens 1154A into a left-hand circular polarized(LHCP) beam 1166A. On the other hand, the waveplate lens 1154A isconfigured to diverge a LHCP light beam 1162A incident on the waveplatelens 1154A into a right-hand circular polarized (RHCP) beam 1166B.

Still referring to FIG. 12A, after being focused or defocused by thewaveplate lens 1154A depending on the circular polarization of the lightincident thereon, the LHCP light beam 1166A or the RHCP light beam 1166Bis incident on a switchable waveplate 1158. The liquid crystals of theswitchable waveplate 1158 are configured such that, when activated,e.g., electrically activated, the polarization of a circularly polarizedlight passing therethrough is preserved (not illustrated). That is, theLHCP light beam 1166A and the RHCP light beam 1166B passes through theswitchable waveplate 1158 unaffected. On the other hand, whendeactivated, e.g., electrically activated, the polarization of thecircularly polarized light passing therethrough is flipped(illustrated). That is, the LHCP light beam 1166A is converted to a RHCPlight beam 1170A and the RHCP light beam 1166B is converted to a LHCPlight beam 1170B.

Referring to FIG. 12B, in some other embodiments, the broadband adaptivelens assembly 1150B is configured to be switched between differentoptical power states by employing a switchable waveplate lens 1154Bcomprising liquid crystals. The adaptive lens assembly 1150B may beselectively switched between different states by electrically activatingand deactivating the switchable waveplate lens 1154B.

In operation, the liquid crystals of the waveplate lens 1154B areconfigured such that the waveplate lens 1154B diverges or converges theincident light 1162A, 1162B passing therethrough depending on itspolarization, e.g., circular polarization, according to variousembodiments. When configured as a half-waveplate lens, when deactivated,e.g., electrically deactivated, the illustrated waveplate lens 1154B isconfigured to converge a RHCP light beam 1162B incident on the waveplatelens 1160B into a LHCP beam 1166A. Conversely, when deactivated, thewaveplate lens 1154B is configured to diverge a left-hand polarized(LHCP) light beam 1162A incident on the waveplate lens 1154B into a RHCPbeam 1166B. On the other hand, when activated, e.g., electricallydeactivated, the polarization of the circularly polarized light passingtherethrough is preserved (not illustrated), and the LHCP light beam1162A and the RHCP light beam 1162B incident thereon pass through thewaveplate lens 1154B without substantially being converged or diverged.In various embodiments, by configuring the liquid crystals to berearranged in response to a switching signal, e.g., electric field, thewaveplate lens assemblies 1150A, 1150B may be activated or deactivatedto converge or diverge and to flip or conserve the polarization ofcircularly polarized light depending on its polarization.

Broadband Switchable Waveplates

As described above, according to various embodiments, the broadbandadaptive waveplate lens assembly can be used to generate images atmultiple depth planes by selectively switching the broadband waveplatelens assembly between a plurality of lens states having differentoptical powers. As described above, in some embodiments, the broadbandadaptive waveplate lens assembly may configured to be selectivelyswitched between a plurality of lens states by electrically activating abroadband switchable waveplate included in the broadband adaptivewaveplate lens assembly. In the following, embodiments of broadbandswitchable waveplates are disclosed.

In some embodiments, a broadband switchable waveplate comprises a layerof unpolymerized twisted nematic (TN) liquid crystals (LCs) and isconfigured to be switched upon application of an electric field across athickness of the layer of TN LCs. Without being bound to any theory, theswitching may be achieved upon altering orientations of theunpolymerized LC molecules across the thickness of the layer of TN LCs.

Referring to FIGS. 13A-13F, according to various embodiments, broadbandswitchable waveplates comprise a layer of twisted nematic (TN) liquidcrystals (LCs). FIG. 13A illustrates a cross-sectional view of anexample of a switchable waveplate comprising a layer of TN LCs. A TN LCswitchable waveplate 1300A comprises a layer 1302 of TN LCs disposedbetween a pair of transparent substrates 1312. Each of the transparentsubstrates 1312 has formed on the inner surface a conducting transparentelectrode 1316, 1320.

The surfaces of the transparent electrodes 1316, 1320 and/or thesubstrates 1312 may be configured such that the TN LC molecules incontact with or immediately adjacent to the upper electrode 1316 tend toorient with their long axes extending in a first lateral direction,while the TN LC molecules in contact with or immediately adjacent to thelower electrode 1320 tend to orient with their long axes extending in asecond lateral direction, which may cross, e.g., to form an angle ofabout 90 degrees relative to, the first lateral direction. The TN LCmolecules between the TN LC molecules immediately adjacent to the lowerelectrode 1320 and the TN LC molecules immediately adjacent to the upperelectrodes 1316 undergo a twist. As configured, the TN LC switchablewaveplate 1300A is configured as a broadband waveplate.

Still referring to FIG. 13A, in operation, in the absence of an electricfield (deactivated state) across the TN LC layer 1302, the nematicdirector of the TN LC molecules undergoes a smooth 90 degree twistacross the thickness of the TN LC layer 1302. In this state, theincident light 1308 polarized in a first direction (same direction asthe LC molecules closest to the lower electrodes 1312) is incident onthe TN LC layer 1302. The twisted arrangement of the TN LC moleculeswithin the TN LC layer 1302 then acts as an optical wave guide androtates the plane of polarization by a quarter turn (90 degrees) priorto reaching the upper electrodes 1316. In this state, the TN LC layer1302 serves to shift the polarization direction of linearly polarizedlight passing therethrough from one linear polarization direction toanother. Thus, the transmitted light 1304 is polarized in a seconddirection (same direction as the LC molecules closes to the upperelectrodes 1316) opposite the first direction.

On the other hand, when a voltage exceeding a threshold voltage (V>Vth)of the TN LC switchable waveplate 1300A is applied to across theelectrodes 1316, 1320 (activated state), the TN LC molecules within theTN LC layer 1306 tend to align with the resulting electric field and theoptical wave guiding property of the TN LC layer 1304 described abovewith respect to the deactivated state is lost. In this state, the TN LClayer 1306 serves to preserve the polarization direction of lightpassing therethrough. Thus, the incident light 1308 and the transmittedlight 1304B are polarized in the same first direction (same direction asthe LC molecules closest to the lower electrodes 1312).

When the electric field is turned off, the TN LC molecules relax back totheir twisted state and the TN LC molecules of the TN LC layer 1306 inthe activated state returns to the configuration of TN LC molecules ofthe TN LC layer 1302 in the deactivated state.

As described above, the TN LC switchable waveplate 1300A described withrespect to FIG. 13A serves to shift the polarization direction oflinearly polarized light. However, various broadband waveplate lensassemblies described herein includes a switchable waveplate configuredas a switchable half waveplate for reversing handedness of circularpolarized light. Thus, in the following with respect to FIGS. 13B-13D,switchable waveplates configured as switchable half waveplates aredescribed, according to embodiments.

FIG. 13B illustrates a cross-sectional view of a switchable broadbandwaveplate 1300B configured as a half wave plate, according toembodiments. The switchable broadband waveplate 1300B includes the TN LCswitchable waveplate 1300A illustrated with respect to FIG. 13A. Inaddition, in order to serve as a broadband half waveplate for circularpolarized light, the switchable broadband waveplate 1300B additionallyincludes a pair of achromatic quarter waveplates (QWP) 1324, 1326.

In operation, in an activated state of the switchable broadbandwaveplate 1300B, when an incident circularly polarized light beam 1324having a first handedness, e.g., a left-hand circular polarized (LHCP)light beam, passes through the first QWP 1324, the first QWP 1324converts the circularly polarized light beam 1324 into a first linearlypolarized light beam 1328 having a first linear polarization.Subsequently, upon passing through an activated TN LC switchablewaveplate 1300A, the first linearly polarized light beam 1328 isconverted into a second linearly polarized light beam 1332 having asecond linear polarization. Subsequently, upon passing through thesecond QWP 1326, the second linearly polarized light beam 1332 istransformed into an exiting circularly polarized light beam 1340 havinga second handedness opposite the first handedness, e.g., into a RHCPlight beam. Thus, when activated, the switchable broadband waveplate1300B serves as a half waveplate that reverses the polarization of acircular polarized light beam.

On the other hand, when the switchable broadband waveplate 1300B isdeactivated, after the incident circularly polarized light beam 1324passes through the first QWP 1324 as described above and subsequentlypasses through a deactivated TN LC switchable waveplate 1300A, thepolarization of the first linearly polarized light beam 1328 ispreserved. Thereafter, upon passing through the second QWP 1326, firstlinearly polarized light beam 1328 is transformed into an exitingcircularly polarized light beam 1340 having the first handedness, e.g.,into a LHCP light beam. Thus, when deactivated, the broadband waveplate1300B serves as transparent medium which preserves the polarization of acircular polarized light beam.

In various embodiments described herein, the first and/or second QWP1324, 1326 are broadband quarter waveplates having similar bandwidthscompared to the TN LC switchable waveplate 1300A. According toembodiments, quarter waveplates can be formed using a polymerized TN LClayer. To provide broadband capability, QWP according to variousembodiments include a plurality of TN LC layers. When each of the TN LClayers are formed on its own substrate, the resulting broadband quarterwaveplate and/or the optical absorption of the resulting stack maybecome unacceptably thick. Thus, in the following, embodiments of QWPscomprising a plurality of TN LC layers formed on a single substrate aredescribed, for efficient integration with the TN LC switchable waveplate1300A.

FIG. 13C illustrates a cross-sectional view of a broadband QWP 1300C,which can be the first and/or second QWP 1324, 1326 illustrated abovewith respect to FIG. 13B, comprising a plurality (M) of TN LC layers1302-1, 1302-2, . . . 1302-M, stacked on an alignment layer 1302-0formed on a substrate 1312. The alignment layer 1302-0, which isdescribed in more detail elsewhere in the specification, is configuredto induce the elongation direction of the LC molecules in the first TNLC layer 1302-1 that are immediately adjacent to the alignment layer1302-0 to be aligned in a first direction. The LC molecules above the LCmolecules aligned by the alignment layer 1302-0 undergo a first twist,such that the LC molecules in the first TN LC layer 1302-1 directlyadjacent to the second TN LC layer 1302-2 are elongated in a seconddirection. The alignment of LC molecules in each of the subsequent TN LClayers 1302-2 to 1302-M are aligned in a similar manner as the first TNLC layer 1302-1 except, the LC molecules closest to the previous layeris aligned in the same direction as the topmost LC molecules of theprevious layer. For example, the topmost LC molecules in the first TN LClayer 1302-1 and the bottommost LC molecules in the second TN LC layer1302-1 are aligned in the same second direction. The LC molecules in thesecond TN LC layer 1302-2 undergo a second twist, such that the topmostLC molecules in the second TN LC layer 1302-2 are elongated in a thirddirection. Such alignment of LC molecules in a given TN LC layer as aresult of the alignment of LC molecules in an adjacent layer in contacttherewith is sometimes referred to as self-alignment, because nointervening alignment layer is interposed therebetween. Thus, in someembodiments, embodiments broadband QWPs comprise a plurality of TN LClayers having two or more self-aligned TN LC layers each having anon-zero twist.

In embodiments, the TN LC layers comprise polymerized LC molecules(LCPs), formed using, e.g., reactive mesogens. As described above,reactive mesogens are initially low molecular weight LCs which may bealigned by surfaces and a twist to have complex profiles, as withconventional LCs, but which may then be cured into a solid polymer filmby photo-polymerization.

FIG. 13D illustrates a cross-sectional view of an integrated switchablebroadband waveplate 1300D in which a TN LC switchable waveplate 1300Asimilar to that described above with respect to FIG. 13A is integratedinto a single stack with a pair of broadband QWP 1324, 1326 similar tothat described above with respect to FIG. 13C. In the illustratedembodiment, the TN LC switchable waveplate 1300A is integrated into asingle stack by having attached on opposing sides thereof the pair ofbroadband quarter waveplates 1324, 1326 using adhesive layers 1348.

FIG. 13E illustrates a cross-sectional view of an integrated switchablebroadband waveplate 1300E in which a TN LC switchable waveplate 1300Asimilar to that described above with respect to FIG. 13A is integratedinto a single stack with a pair of broadband quarter waveplates 1324,1326 in a similar manner as described above with respect to FIG. 13D,except, instead of using adhesive to form an integrated stack, one ofthe pair of broadband quarter waveplates 1324, 1326 serves as asubstrate on which a TN LC switchable waveplate 1300A (FIG. 13A) may bedirectly formed. For example, on a surface of one of the QWP 1324, 1326,different layers of the TN LC switchable waveplate 1300A may be directlyformed. Advantageously, one or both of the substrates 1312 of the TN LCswitchable waveplate 1300A may be omitted. Thus, the TN LC switchablewaveplate 1300A is integrated into a compact single stack by beingdirectly formed on one of the pair of broadband QWP 1324, 1326, andforming thereon the other one of the pair of broadband QWP 1324, 1326.

In each of the embodiments illustrated above with respect to FIGS. 13Dand 13E, the broadband QWP can be formed of liquid crystal-basedmaterials or other non liquid crystal-based materials such as, e.g.,quartz and MgF₂. In the following, with respect to FIG. 13F, anembodiment in which broadband QWP comprising liquid crystals isparticularly advantageously integrated with a TN LC switchable waveplateinto a single stack to serve not only as QWP but also as alignmentlayers for the TN LC switchable waveplate.

FIG. 13F illustrates a cross-sectional view of an integrated switchablebroadband waveplate 1300F integrating a TN LC switchable waveplate 1300Asimilar to that described above with respect to FIG. 13A. The switchablebroadband waveplate 1300F includes a pair of broadband QWP 1324, 1326arranged in a similar manner as described above with respect to FIG.13E, except, instead of the broadband QWP 1324, 1326 as substrates forthe TN LC layer 1302, broadband QWP 1324, 1326 comprising thinpolymerized LC layers formed on respective surfaces of substrates 1312,and LC molecules of the TN LC layer 1302 are inserted into a gap formedbetween opposing surfaces of broadband QWP 1324, 1326 by spacers 1350,which defines the thickness of the TN LC layer 1302. The method ofinserting the LC molecules is described elsewhere in the specification.In addition, different layers of the TN LC switchable waveplate 1300Aand different layers of the broadband QWP 1324, 1326 are integrallyformed into a single stack. For example, the first broadband QWP 1324includes a substrate 1312 on which a lower transparent electrode 1316 isformed, followed by an alignment layer 1302-2 and a plurality of TN LClayers 1302-1, 1302-2. Similarly, the second broadband QWP 1326 includesa substrate 1312, on which an upper transparent electrode 1320 isformed, followed by an alignment layer 1302-0 and a plurality of TN LClayers 1302-1, 1302-2.

Still referring to FIG. 13F, advantageously, the outermost LC moleculesof the TN LC layer 1302-2 of the first broadband QWP 1324 facing the gapand the outermost LC molecules of the TN LC layer 1302-2 of the secondbroadband QWP 1326 facing the gap are arranged to serve as alignmentlayers for the switchable TN LC layer 1302, such that the outermost LCmolecules of the TN LC layer 1302 are self-aligned, in a similar manneras described above with respect to FIG. 13C. In addition, by integrallystacking different layers the TN LC switchable waveplate 1300A withdifferent layers of the broadband QWP 1324, 1326, the total thickness ofthe entire stack can be substantially reduced. For instance, whilemechanically bonding TN LC switchable waveplate 1300A as illustrated inFIG. 13A with the broadband quarter waveplates 1324, 1326 as illustratedin FIG. 13C would have resulted in as many as four substrates, theentire stack of the switchable broadband waveplate 1300F has only twosubstrates.

In references to FIG. 13F and various embodiments throughout thespecification, a switchable LC layer, e.g., the TN LC layer 1302inserted into the gap has a thickness of about 1 μm-50 μm, 1-10 μm,10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm or a value within any rangedefined by these values. In addition, passive LC layers, e.g., the TN LClayers 1302-1, 1302-2, can have a thickness of about 0.1 μm-50 μm, 0.1-1μm, 1-10 μm, 10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm or a value withinany range defined by these values.

In various embodiments described herein, an alignment layer (e.g.,1302-2 in FIGS. 13C, 13F) is used to align LC molecules, e.g., align theelongation direction of LC molecules, along a particular direction. Forexample, as described above with respect to FIGS. 13A-13F, an alignmentlayer can be used to define a director (n), or a local averageelongation direction of elongated LC molecules, in a predetermineddirection. In some other embodiments, an alignment layer may be formedof organic polymers such as polyimides and polyamides that aremechanically rubbed, obliquely deposited inorganic oxides such as SiO₂,or long chain aliphatic siloxanes. In some embodiments, a noncontactalignment layer may be formed of organic polymers using plane-polarizedlight to generate a surface anisotropy, which turn defines the director.For example, use of cis-trans photoisomerization of azo dye, which maybe deposited directly or dissolved into a standard orientation layer(e.g., polyimide) or the LC mixture, can produce an orientation effectin the alignment layer without rubbing. Noncontact alignment layers thatuse azo chromophores sometimes employ an intense laser light to inducethe isomerization of the dye molecules.

In some other embodiments, a pattern of nanostructures can serve as analignment layer for aligning the LC molecules. Advantageously, in someembodiments, the pattern of nanostructures can be formed as part of anelectrode layer to improve optical transmittance, to reduce processsteps, and to further reduce the overall thickness of the broadbandwaveplates described above, e.g., with respect to FIGS. 13A-13F. Toachieve this end, FIG. 14A illustrates perspective view of a pattern ofnanostructures 1400A, e.g., nanowires formed on a transparent substrate1312, that serve a dual function of an alignment layer as well as anelectrode layer, according to embodiments. The pattern of nanostructures1400A can be patterned on the substrate 1312 using, e.g., a lithographicor a nanoimprinting technique, described in detail elsewhere in thespecification. The nanostructures can be formed of a sufficiently thinconducting material that is patterned as elongated metal wires. Forexample, the conducting material can be gold, silver, copper, aluminumor ITO or any suitable conducting material having a thickness andelectrical resistivity such that the resulting pattern of nanostructurescan serve simultaneously as an alignment layer and as an electrodelayer. In the illustrated embodiment, the pattern of nanostructures1400A comprises periodic conducting lines 1404A extending in a firstdirection, e.g., x-direction, that are connected to a rail 1408A forsupplying current or voltage to the periodic conducting lines 1404A. Invarious embodiments, the periodic conducting lines 1404A can have apitch of 1 μm to 1000 μm, 5 μm to 500 μm, 10 μm to 100 μm, or any valuewithin a range defined by these values. The conducting lines 1404 canhave a width of 10 nm to 1 μm, 100 nm to 1000 nm, 100 nm to 500 nm, 200nm to 300 nm, or any value within a range defined by these values. Theperiodic conducting lines 1404 can have a thickness of 10 nm to 1 μm,100 nm to 1000 nm, 100 nm to 500 nm, 400 nm to 500 nm, or any valuewithin a range defined by these values. A combination of the material,the thickness and the width of the periodic conducting lines 1404A canbe selected such that a resulting sheet resistance of the periodicconducting lines 1404A is about 1 Ohms/square to 100 Ohms/square, 2Ohms/square to 50 Ohms/square, 5 Ohms/square to 20 Ohms/square, or anyvalue within a range defined by these values, for instance about 10Ohms/square. In addition, a combination of the material and thickness ofthe conducting lines 1404A can be selected such that the resultingtransmittance in the visible spectrum is 80% to 99%, 90% to 99%, 95% to99%, 97% to 99%, or any value within a range defined by these values,for instance about 98%. Other dimensions, configurations and values arepossible.

FIG. 14B illustrates a perspective view of a pattern of nanostructures1400B that is similar to the pattern of nanostructures 1400A describedabove with respect to FIG. 14A, except, the pattern of nanostructures1400B comprises periodic conducting lines 1404B extending in a seconddirection, e.g., y-direction, that are connected to a rail 1408B forsupplying current to the periodic conducting lines 1404B.

FIG. 14C illustrates a perspective view of a pair of electrodes 1400C,according to embodiments. The pair of electrodes 1400C includes thepattern of nanostructures 1400A and the pattern of nanostructures 1400Barranged such that the periodic conducting lines 1404A and the periodicconducting lines 1404B face and cross each other, and are separated by agap 1412 configured to dispose one or more LC layers, e.g., TN LClayers, therein. Advantageously, it has been found that each of thepatterns of nanostructures 1400A and 1400B can serve as an alignmentlayer similar to the alignment layer 1302-0 described above with respectto FIGS. 13C, 13F such that when nematic LC molecules, e.g., reactivemesogens, are formed thereon, the LC molecules that are immediatelyadjacent to each of the patterns of nanostructures 1400A and 1400B maybecome aligned, e.g., with the director of the nematic LC moleculesgenerally being aligned in the same direction as the elongationdirection of the periodic conducting lines 1404A, 1404B. In addition,the LC molecules between the LC molecules immediately adjacent to theperiodic conducting lines 1404A, 1404B can be configured to undergo atwist using a twisting agent such that an unpolymerized TN LC layerssimilar to the TN LC layer 1302 described above with respect to FIG. 13Aand polymerized TN LC layer(s) similar to the TN LC layers 1302-1,1302-2, . . . 1302-M described above with respect to FIG. 13C may beformed.

Referring back to FIG. 13F, it will be appreciated that, in someembodiments, by combining the functionality of an electrode and analignment layer, the pattern of nanostructures 1400A can replace thecombination of the transparent electrode 1316 and the alignment layer1302-0 of the broadband QWP 1324, and the pattern of nanostructures1400B can replace the combination of the transparent electrode 1320 andthe alignment layer 1302-0 of the broadband QWP 1326, thereby allowing amore compact overall stack.

Still referring to FIG. 14C, in operation, the arrangement of LCmolecules with and without an electric field and the correspondingeffect on the polarization of light is similar to that described abovewith respect to FIG. 13A.

FIGS. 15A and 15B illustrate a plan view and a cross-sectional view of aTN LC switchable broadband waveplate 1500, according to embodiments.Unlike the broadband waveplates illustrated above with respect to FIGS.13A, 13F having vertically separated electrodes for switching, the TN LCswitchable broadband waveplate includes an in-plane laterally separatedelectrodes for switching. The TN LC switchable broadband waveplate 1500includes an alignment electrode stack 1524 and an alignment layer stack1526. In a similar manner as described above with respect to FIG. 13F,LC molecules are inserted into a gap formed by spacers 1350 betweenopposing surfaces of the alignment electrode stack 1524 and thealignment layer stack 1526. The method of inserting the LC molecules isdescribed elsewhere in the specification. The alignment electrode stack1524 includes first and second electrodes 1500A, 1500B formed on anupper transparent substrate 1312, and further includes an optional upperalignment layer 1302-0. The alignment layer stack 1526 includes a loweralignment layer 1302-0 formed on a lower transparent substrate 1312.

Referring to FIG. 15A, the alignment electrode stack 1524 includes thefirst and second electrodes 1500A, 1500B each including a respective oneof first and second periodic conducting lines 1504A, 1504B. The periodicconducting lines 1504A are interdigitated or interlaced and alternatingwith the periodic conducting lines 1504B. Each of the first and secondperiodic conducting lines 1504A, 1504B are strapped to rails 1508A,1508B, respectively, in a similar manner as described above with respectto the patterned nanostructures 1400A (FIG. 14A), 1400B (FIG. 14B). Thematerial, thicknesses, widths and the pitch of the alternating periodicconducting lines 1504A, 1504B can be similar to those described abovewith respect to the patterned nanostructures 1400A (FIG. 14A), 1400B(FIG. 14B). However, unlike the pair of electrodes 1400C described abovewith respect to FIG. 14C that are vertically separated, the periodicconducting lines 1504A are alternating with the periodic conductinglines 1504B in a lateral direction, e.g., x-direction, such that theelectric field between the periodic conducting lines 1504A and theperiodic conducting lines 1504B is directed in the lateral direction.

Referring to the cross-sectional view of the TN LC switchable cell 1500in FIG. 15B, in a similar manner as described above with respect to FIG.13F, LC molecules are inserted into the gap formed between opposingsurfaces of the alignment electrode stack 1524 and the alignment layerstack 1526, such that a TN LC layer (not shown) similar to the TN LClayer 1302 (FIG. 13A) can be formed. The method of inserting the LCmolecules is described elsewhere in the specification.

In some embodiments, in a similar manner as described above with respectto FIG. 14C, the alternating periodic conducting lines 1504A, 1504Band/or the upper alignment layer 1302-0 in the alignment electrode stack1524 can serve as alignment layers for outermost LC molecules of a TN LClayer 1302 formed in the gap 1412, in a similar manner as the alignmentlayer 1316 described above with respect FIG. 13A and to the conductinglines 1404B described above with respect FIG. 14C. When the alternatingperiodic conducting lines 1504A, 1504B serve as an alignment layer, insome embodiments, the upper alignment layer 1302-0 may be omitted. In asimilar manner to the alignment layer 1320 described above with respectFIG. 13A and to the conducting lines 1404A described above with respectFIG. 14C, the lower alignment layer 1302-0 may serve to align LCmolecules in the gap 1412 that are immediately adjacent thereto.

While not illustrated, in some embodiments, the illustrated TN LCswitchable broadband waveplate 1500 can integrate, in a similar manneras described above with respect to FIG. 1300F, a plurality of TN LClayers similar to the TN LC layers 1302-1, 1302-2, . . . 1302-M (FIG.13F, not shown) between the alternating periodic conducting lines 1504A,1504B and the LC molecules in the gap 1412, and/or between the loweralignment layer 1302-0 and the LC molecules in the gap 1412, therebyproviding an integrated QWP functionality in a similar manner asdescribed above with respect to FIG. 13F.

Still referring to FIGS. 15A, 15B, in operation, in the absence of anelectric field, the alternating periodic conducting lines 1504A, 1504Bserve as an alignment layer for the LC molecules immediately adjacent tothe periodic conducting lines 1504A, 1504B, such that the LC moleculeshave a director generally extending parallel to the periodic conductinglines 1504A, 1504B. In the deactivated state, in a similar manner asdescribed above with respect to FIG. 13A, the switchable broadbandwaveplate 1500 is configured to flip the polarization of linearlypolarized light. On the other hand, when an electric field is applied ina lateral direction, e.g., y-direction, between the periodic conductinglines 1504A and the periodic conducting lines 1504B, the LC moleculesbetween immediately adjacent periodic conducting lines 1504A, 1504Balign with their elongation direction in a direction away from parallel,e.g., between parallel and perpendicular or perpendicular, to theperiodic conducting lines 1504A, 1504B. In the activated state, in asimilar manner as described above with respect to FIG. 13A, theswitchable broadband waveplate 1500 is configured to preserve thepolarization of linearly polarized light.

In some embodiments, in addition to combining the functionality ofelectrodes and an alignment layer, the first and second electrodes1500A, 1500B can, e.g., replace the combination of the transparentelectrodes 1316, 1320 and the upper and lower alignment layers 1302-0 ofthe broadband waveplate 1300F (FIG. 13F), thereby allowing a furthermore compact overall stack, and even more improved transmittance due tohalving of electrode layers.

Liquid Crystal-Based Waveplate Lenses

As described above with respect to FIG. 12A, to provide images at aplurality of depth planes with high efficiency over a wide range of thevisible spectrum, some broadband adaptive waveplate lens assembliesaccording to embodiments include a switchable waveplate and one or morewaveplate lenses, which may be passive or switchable, that are formed ofa thin film of birefringent liquid crystals. In the following, examplewaveplate lenses comprising liquid crystals whose orientations in theplane of the waveplate are adapted for focusing and/or altering thepolarization state of light transmitted therethrough are disclosed. Inthe following, various embodiments of lenses and waveplates formed ofliquid crystals.

One example of liquid crystal-based waveplate lenses is illustrated withrespect to FIGS. 16A and 16B.

FIGS. 16A and 16B illustrate examples of waveplate lenses 1200A and1200B, respectively, each comprising a transparent substrate 1204, e.g.,a glass substrate, having formed thereon liquid crystal molecules 1208elongated along different elongation directions relative to a directionparallel to an axial direction (e.g., x-direction or y-direction) alonga major surface of the substrate 1204. That is, the liquid crystalmolecules 1208 are rotated about a direction (e.g., z-direction) normalto a major surface of the substrate 1204 by different angles (q) ofrotation, where φ is described as the angle between the direction ofelongation of the liquid crystal molecules relative to a directionparallel to the layer normal (e.g., x-direction or y-direction).

In the illustrated implementations, the liquid crystal molecules 1208 ata given radius from a central axis C or the center of the lens have thesame angle (φ) of rotation. As arranged, the liquid crystal molecules1208 are configured to focus a collimated beam of light to a point at afocal length. Without being bound to any theory, the angle (φ) ofrotation of liquid crystal molecules 1208 may be proportional to a powerof r, where r is the radial distance from C and has a value betweenabout 1 and 3, e.g., 2. In one implementation, the angle (φ) may beproportional to +/−k₀r²/f, where r is the radial distance from C andk₀=2π/λ is the wavenumber of the light that is to be focused by thediffractive waveplate lens, λ is the wavelength of the light, f is thefocal length of the waveplate lenses 1200A, 1200B. The + and −sign cancorrespond to the direction of rotation of the liquid crystal molecules1208 relative to the liquid crystal molecules 1208 nearest to the centerC of the waveplate lenses 1200A, 1200B.

It will be appreciated that the patterns of liquid crystal molecules1208 of waveplate lenses 1200A and 1200B represent flipped images ofeach other. That is, one of the waveplate lenses 1200A and 1200B may beobtained by rotating the other of the waveplate lenses 1200B and 1200Baround an axial direction (e.g., x-direction or y-direction) by 180degrees. As configured, focal lengths and optical powers of thewaveplate lenses 1200A and 1200B are the same in magnitude but oppositein sign.

In some implementations, each of waveplate lenses 1200A and 1200B mayserve as half waveplate lenses. When configured as a half-waveplatelens, each of the waveplate lenses 1200A and 1200B rotates the plane ofa linearly polarized light by an angle 2 a with respect to thepolarization of an input beam, where a is the angle between the inputpolarization direction and the waveplate axis. For a circular polarizedbeam, this change in angle translates into a phase shift and reversal ofthe polarization handedness. Thus, a ±2α phase shift may be generated ina circularly polarized beam with the sign of the phase shift dependingon the polarization handedness.

FIG. 16C illustrates examples of a waveplate lens that diverges orconverges light passing therethrough depending on the polarization oflight and the side on which the light is incident, according to someembodiments. When configured as a half-waveplate lens, the illustratedwaveplate lens 1200A may be configured to diverge a right-hand circularpolarized (RHCP) light beam 1212 incident on a first side into aleft-hand circular polarized (LHCP) beam 1216. On the other hand, thewaveplate lens 1200A may be configured to converge a RHCP light beam1220 incident on a second side opposite to the first side into aleft-hand circular polarized (LHCP) beam 1224.

For the waveplate lens 1200B, the situation is reversed. As illustratedin FIG. 16D, when configured as a half-waveplate, the waveplate lens1200B may be configured to converge a LHCP light beam 1228 incident on afirst side into a RHCP beam 1232. On the other hand, the waveplate lens1200B may be configured to diverge a LHCP light beam 1236 incident on asecond side opposite the first side into a RHCP beam 1240.

Thus, by controlling the direction of angle of rotation and the radialdistribution of the liquid crystals 1208, the waveplate lens may beconfigured to converge or diverge circularly polarized light havingeither handedness. It will be appreciated that, based on therelationship between the angles of rotation of the liquid crystals, theoptical power may be increased or decreased. In addition, in someembodiments, the liquid crystals may be aligned and unaligned byapplying an electric field. Thus, it will be appreciated that in thelimit where the optical power is near zero, the waveplate lenses may beused as waveplates, e.g., switchable waveplates.

Broadband Adaptive Waveplate Lens Assemblies Including a SwitchableWaveplate

As described above with respect to FIG. 12A, to provide images at aplurality of depth planes with high efficiency over a wide range of thevisible spectrum, some broadband adaptive waveplate lens assembliesaccording to embodiments include a switchable waveplate and one or morewaveplate lenses, which may be passive or switchable, that are formed ofa thin film of birefringent material, e.g., liquid crystals. In thefollowing, embodiments of broadband adaptive waveplate lens assembliescomprising a switchable broadband waveplate are disclosed. For example,the switchable broadband waveplate may be one of broadband switchablewaveplates described above with respect to FIGS. 13A-13F, FIGS. 14A-14Cand FIGS. 15A-15B.

FIG. 17A illustrates an example of a broadband adaptive waveplate lensassembly 1700 comprising waveplate lenses, e.g., passive waveplatelenses, and a switchable waveplate, according to some embodiments. Thebroadband adaptive waveplate lens assembly 1700 may be configured, e.g.,as either one of the pair of switchable waveplate assemblies 1004, 1008described supra with respect to FIGS. 10, 11A and 11B. FIG. 17Billustrates the broadband adaptive waveplate lens assembly 1700A inoperation when the switchable waveplate of the adaptive lens assembly1700 illustrated in FIG. 17A is activated, whereas FIG. 17C illustratesthe broadband adaptive waveplate lens assembly 1700B in operation whenthe switchable waveplate of the adaptive lens assembly 1700 illustratedin FIG. 17A is deactivated. The adaptive lens assembly 1700 isconfigured to couple and to transmit therethrough the light outcoupledfrom the waveguide assembly 1012 (FIGS. 10, 11A, 11B). The adaptive lensassembly 1700 comprises a first waveplate lens (L1/HWP1) 1704, e.g., afirst half-waveplate lens, a second waveplate lens (L2/HWP2) 1708, e.g.,a second half-waveplate lens, and a switchable waveplate (HWP3) 1712,e.g., a switchable half waveplate.

In various embodiments, each of the L1/HWP1 1704 and L2/HWP2 1708 isconfigured to serve as a lens and a half waveplate. As described abovewith respect to FIGS. 12A and 12B, when configured as a half-waveplate,each of the L1/HWP1 1704 and L2/HWP2 1708 is configured to convert lighthaving a circular polarization of first handedness (first HCP) to lighthaving a circular polarization of second handedness (second HCP). Thatis, each of the L1/HWP1 1704 and L2/HWP2 1708 is configured to convertlight passing therethrough from light having LHCP or RHCP, and toconvert light having RHCP or LHCP, respectively.

In various embodiments, each of the L1/HWP1 1704 and L2/HWP2 1708 isconfigured to serve as a lens, for a given polarization, having a firstlensing effect or a second lensing effect opposite the second lensingeffect. That is, each of the L1/HWP1 1704 and L2/HWP2 1708 is configuredto either converge or diverge light passing through. In variousembodiments, each of the L1/HWP1 1704 and L2/HWP2 1708 may be configuredto have opposite lensing effects depending on the polarization state ofthe incident light. For example, each of the L1/HWP1 1704 and L2/HWP21708 may be configured to focus light incident thereon having a firstHCP while being configured to defocus light incident thereon having asecond HCP.

In some embodiments, the L1/HWP1 1704 and L2/HWP2 1708 are configured tohave the same lensing effect for light having a given HCP. That is, bothof the L1/HWP1 1704 and L2/HWP2 1708 may be configured to focus lighthaving LHCP, focus light having RHCP, defocus light having LHCP ordefocus light having RHCP.

In some embodiments, each of the L1/HWP1 1704 and L2/HWP2 1708 maycomprise liquid crystal molecules that are elongated and rotated suchthat liquid crystals at a given radius from a central axis of therespective waveplate lenses 1704, 1708 have the same angle (φ) ofrotation, as described above with respect to FIGS. 12A and 12B. Each ofthe first and second waveplate lenses 1704, 1708 is configured to altera polarization state, e.g., invert a polarization state, of lightpassing therethrough. The switchable waveplate 1712 is configured toalter a polarization state, e.g., invert a polarization state, of lightpassing therethrough when electrically deactivated, while beingconfigured to substantially pass light without altering the polarizationstate of light passing therethrough when activated. The electricalsignal, e.g., a current signal or a voltage signal, for switching theswitchable waveplate 1712 may be provided by a switching circuit 1716electrically connected thereto.

In various embodiments, when deactivated, e.g., electrically deactivatedusing a voltage or a current signal provided by the switching circuit1716, the HWP3 1712B (FIG. 17C) serves as a half waveplate. That is,when deactivated, the HWP3 1712B (FIG. 17C) serves as a half waveplateconfigured to convert light passing therethrough from light having LHCPor RHCP to light having RHCP or LHCP, respectively. Thus, each of theL1/HWP1 1704, the L2/HWP2 1708, and the HWP3 1712B when deactivated(FIG. 17C) is configured to convert light having a circular polarizationof first handedness (first HCP) to light having a circular polarizationof second handedness (second HCP).

In various embodiments, when activated, e.g., electrically activatedusing a voltage or a current signal provided by the switching circuit1716, e.g., by removing the voltage or the current signal, the HWP31712A (FIG. 17B) serves as transmitting medium for light withoutaffecting the polarization or providing any lensing effect.

In some embodiments, a single waveplate lens 1704 and/or 1708 mayfunction both as a waveplate lens and as a switchable half waveplate. Insuch embodiments, the dedicated switchable half waveplate 1712 may beomitted.

FIG. 17B illustrates an example of the adaptive lens assembly of FIG.17A in operation with the switchable waveplate activated, according tosome embodiments. The adaptive lens assembly 1700A may be activated whenthe switchable waveplate 1712 is activated, e.g., when no current orvoltage is applied to the switchable waveplate 1712 by the switchingcircuit 1716. The adaptive lens assembly 1700A may correspond to thefirst adaptive lens assembly 1004 (on the world side) or the secondadaptive lens assembly 1008 (on the user side). By way of example only,the adaptive lens assembly 1700A will be described as corresponding tothe first adaptive lens assembly 1004 or the second adaptive lensassembly 1008, as part of the display device 1000 (FIG. 10) that isdisplaying the view of the real world to the user without displaying avirtual image. For example, the display device 1000 (FIG. 10) may beused as an ordinary eyeglass or an ordinary goggle. Each of the L1/HWP11704 and L2/HWP2 1708 may be configured to have a first lensing effect,e.g., diverging effect, on light having a first HCP, e.g., LHCP, passingtherethrough. Each of the L1/HWP1 1704 and L2/HWP2 1708 may also beconfigured to have a second lensing effect opposite the first lensingeffect, e.g., converging effect, on light having the opposite HCP, e.g.,RHCP, passing therethrough.

In the illustrated embodiment, the light beam 1720 may represent a lightbeam from the world that is incident on either the first adaptive lensassembly 1004 (on the world side) or the second adaptive lens assembly1008 (on the user side) while the display device 1700A is being used asordinary eyeglasses or a goggle, without displaying virtual content. Byway of example only, the light beam 1720 having a first HCP, e.g., LHCP,travels, e.g., in a positive z-direction, until the beam 1720 impingeson the L1/HWP 1704, to be transmitted therethrough. The L1/HWP1 1704converts the light beam 1720 having LHCP into a light beam 1724 havingRHCP. Because the L1/HWP1 1704 is also configured as a lens, the L1/HWP11704 also diverges the light beam 1720 according to a first opticalpower P1 of the L1/HWP1 1704.

The light beam 1724 having RHCP is subsequently incident on the HWP31712A in the activated state. Because the HWP3 1712A is activated, thelight beam 1724 having RHCP transmits through the HWP3 1712A withoutbeing substantially affected in terms of polarization or lensing effect,to be incident on the L2/HWP2 1708, as light beam 1728A having RHCP. Asdescribed above, when configured as an adaptive lens assembly on theuser side (e.g., second adaptive lens assembly 1004 in FIG. 10), theL2/HWP2 1708 is configured similarly to L1/HWP1 1704 in the illustratedembodiment, i.e., to convert the polarization and to diverge lighthaving LHCP while converging light having RHCP. Thus, the light beam1728A having RHCP is converted back to light beam 1732 having LHCP.Thus, when HWP3 1712A is activated, the L1/HWP1 1704 and the L2/HWP21704 transmit light beams having opposite polarizations, such that theL1/HWP1 1704 and the L2/HWP2 1708 have opposite lensing effect on lightpassing therethrough. That is, because the light beam 1728A incident onthe L2/HWP2 1704 has RHCP, the light beam 1732A exiting the L2/HWP2 1708is converged according to a second optical power P2, unlike the lightbeam 1724 exiting the L1/HWP1 1704 that is diverged according to a firstoptical power P1. Thereafter, upon exiting the adaptive lens assembly1700A in the activated state, the light beam 1732A may be viewed by theeye.

In some embodiments, when the HWP3 1712A is activated, the first opticalpower P1 of L1/HWP1 1704, which may be negative (i.e., diverging), andthe second optical power P2 of L2/HWP2 1708, which may be positive(i.e., converging), may have substantially the same or matchedmagnitudes. In these embodiments, the net optical power Pnet of theadaptive lens assembly 1700A, which may be approximately −P1+P2, may besubstantially zero because of the compensation of the lensing effects ofthe L1/HWP1 1704 and the L2/HWP2 1708. However, embodiments are not solimited, and the first and second optical powers P1, P2 may havedifferent magnitudes, such that the net optical power Pnet may have anonzero value. For example, in some embodiments, the nonzero Pnet may beequal to an eyeglass prescription of the user, thereby allowing forcorrections to focusing errors (e.g., refractive focusing errors) of theeyes of the user.

It will be appreciated that, while in the illustrated embodiment, theincident light beam 1720 has LHCP, a similar outcome would result whenthe incident light beam 1720 has RHCP. That is, when the light beam 1720has RHCP, the light beams 1724 and 1728A have LHCP, and unlike theillustrated embodiment, the light beams 1724 and 1728A are convergedrelative to the light beam 1720. Likewise, the L2/HWP2 1708 diverges thelight beam 1728A converged by the L1/HWP1 1704, such that the netoptical power Pnet may be substantially zero.

It will be appreciated that the lensing effects of the L1/HWP1 1704 andL2/HWP2 1708 and the selectivity of the lensing effects to thepolarization state of incident light beams described above with respectto FIG. 17B serves as but one example, and other configurations arepossible. For example, while in FIG. 17B, the L1/HWP1 1704 and L2/HWP21708 is configured to diverge light having LHCP while converging lighthaving RHCP, in other embodiments, the L1/HWP1 1704 and L2/HWP2 1708 maybe configured to converge light having LHCP while diverging light havingRHCP.

In summary, in some embodiments, when the HWP3 1712A of the adaptivelens assembly 1700A is in a activated state, the exiting light beam1732A has the same HCP as the incident light beam 1720, and may besubstantially matched to the incident light beam 1720 in terms of thelens effect because of the compensation of the lens effects between P1of L1/HWP1 1704 and P2 of L2/HWP2 1708. As a result, when the user isnot viewing virtual content, the view of the world is relativelyunaffected by the presence of the adaptive lens assemblies (1004, 1008in FIGS. 10, 11A, 11B).

FIG. 17C illustrates an example of the adaptive lens assembly of FIG.17A in operation with the switchable waveplate deactivated, according tosome embodiments. The adaptive lens assembly 1700B may be deactivatedwhen the switchable waveplate 1712B is deactivated, e.g., when a currentor a voltage is applied to the switchable waveplate 1712B by theswitching circuit 1716. The adaptive lens assembly 1700B may, e.g.,correspond to the first adaptive lens assembly 1004 (on the world side)or the second adaptive lens assembly 1008 (on the user side). In thefollowing, by way of example, the adaptive lens assembly 1700B will befirst described as being configured as the second adaptive lens assembly1008 on the user side, as part of the display device (e.g., displaydevice 1100A in FIG. 11A) that is outputting virtual image to the user.Subsequently, the adaptive lens assembly 1700B will be described asbeing configured as the first adaptive lens assembly 1004 on the worldside, as part of the display device 1100B (FIG. 11B) that issimultaneously transmitting the view of the real world while outputtingthe virtual image to the user, to reduce or essentially eliminatedistortion of the view of the real world resulting from the lens effectsof the second adaptive lens assembly 1008.

When configured as the second adaptive lens assembly 1008 on the userside (FIG. 11A), each of the L1/HWP1 1704 and L2/HWP2 1708 may beconfigured to diverge light having one of HCP, e.g., LHCP, passingtherethrough. Each of the L1/HWP1 1704 and L2/HWP2 1708 may also beconfigured to converge light having the other HCP, e.g., RHCP, passingtherethrough.

As described above with respect to FIG. 11A, some of the lightpropagating in the x-direction, e.g., by total internal reflection,within the waveguide assembly 1012 may be redirected, or out-coupled, inthe z-direction. The light out-coupled from the waveguide assembly 1012(FIG. 11A) may be incident on the switchable lens assembly 1700B as acircularly polarized light beam 1720 having LHCP. The light beam 1720travels, e.g., in a positive z-direction, until the light beam 1720impinges on the L1/HWP 1704, to be transmitted therethrough. The L1/HWP11704 converts the light beam 1720 having LHCP into a light beam 1724having RHCP. Because the L1/HWP1 1704 is configured to diverge lighthaving LHCP, the light beam 1724 is also diverged according to the firstoptical power P1 of the L1/HWP1 1704.

The light beam 1724 having RHCP is subsequently incident on the HWP31712B in the deactivated state. Unlike the activated HWP 1712Aillustrated above with respect to FIG. 17B, because the HWP3 1712B isdeactivated, the light beam 1724 having RHCP transmitting through theHWP3 1712B is converted to light beam 1728B having LCHP. Subsequently,the light beam 1728B having LHCP is incident on the L2/HWP2 1708.Because, unlike the light beam 1728A illustrated above with respect toFIG. 17B, the light beam 1728B incident on the L2/HWP2 1708 has LHCP,the L2/HWP2 1708 further diverges the light beam 1728B according to asecond optical power P2 into light beam 1732B having RHCP. That is,unlike the activated state of HWP 1712A illustrated with respect to FIG.17B, because the HWP 1712B is deactivated, L1/HWP1 1704 and the L2/HWP11704 are configured to transmit light beams having the samepolarization, LHCP. Thus, unlike the L1/HWP1 1704 and the L2/HWP2 1708having the compensating effect illustrated with respect to FIG. 17B, theL1/HWP1 1704 and the L2/HWP2 1708 in FIG. 17C have additive lensingeffect on the light passing therethrough. That is, because the lightbeam 1720 incident on L1/HWP1 and the light beam 1728B incident onL2/HWP2 1704 both have LHCP, light beam 1732B exiting the L2/HWP2 1708will be further diverged, in addition to being diverged by the L1/HWP11704. Thereafter, upon exiting the adaptive lens assembly 1700B in thedeactivated state, the light beam 1732A may be viewed by the eye.

In some embodiments, the first optical power P1 of L1/HWP1 1704 and thesecond optical power P2 of L2/HWP2 1708 may both be negative (i.e.,diverging) and may have substantially the same or matched magnitudes. Inthese embodiments, the net optical power Pnet of the adaptive lensassembly 1700B, which may be approximately P1+P2, may be substantiallydouble that of P1 or P2 because of the additive lens effect of thecombination of L1/HWP1 1704 and L2/HWP2 1708. However, embodiments arenot so limited, and the first and second optical powers P1, P2 may havedifferent magnitudes.

It will be appreciated that, while in the illustrated embodiment, theincident light beam 1720 has LHCP, parallel outcome will result when theincident light beam 1720 has RHCP. That is, when the light beam 1720 hasRHCP, unlike the illustrated embodiment, the resulting light beam 1732Bhas LHCP and is converged by L1/HWP1 1704 and L2/HWP2 1708 according toa net optical power Pnet, which has a magnitude that is approximately asum of the magnitudes of the first and second optical powers P1 and P2.

It will be appreciated that the lensing effects of the L1/HWP1 1704 andL2/HWP2 1708 and the dependence of the lensing effects on thepolarization state of incident light beams described above with respectto FIG. 17C serves as but one example, and other configurations arepossible. For example, while in FIG. 17B, the L1/HWP1 1704 and L2/HWP21708 are configured to diverge light having LHCP while converging lighthaving RHCP, in other embodiments, the L1/HWP1 1704 and L2/HWP2 1708 maybe oppositely configured to diverge light having LHCP while converginglight having RHCP.

Consequently, in some embodiments, when the switchable half waveplate1712B of the adaptive lens assembly 1700B is in an deactivated state,the exiting light beam 1732B has the opposite HCP relative to theincident light beam 1720, and may be diverged according to additiveoptical powers P1 of L1/HWP1 1704 and P2 of L2/HWP2 1708. As a result,when the user is viewing a virtual content, the virtual content isfocused into the eye 210 according to a net optical power whose value isapproximately Pnet=P1+P2.

In the above, the adaptive lens assembly 1700B in the deactivated statehas been described when configured as the second adaptive lens assembly1008 on the user side in the display device 1100A described supra withrespect to FIG. 11A. As described supra with respect to FIG. 11B,however, activating the second adaptive lens assembly 1008 to displayvirtual content to the user's eye 210, without any compensating effect,may result in a defocusing or distortion of the view of the real world,which may be undesirable. Thus, it may be desirable to configure thefirst adaptive lens assembly 1004 on the world side to at leastpartially compensate or negate the lens effect of the second adaptivelens assembly 1008 when deactivated to display the virtual content.

Referring back to FIG. 17C, when configured as the first adaptive lensassembly 1004 (FIG. 11B) on the world side to negate the lens effect ofthe second adaptive lens assembly 1008 (FIG. 11B) on the user side,components of the adaptive lens assembly 1700B may be configuredsimilarly as described supra with respect to FIG. 11B. That is, as lighttransmitted from the world 510 to the eye 210 traverses the first andsecond adaptive lens assemblies 1004, 1008, each may be configured asdescribed above with respect to the adaptive lens assembly 1700Bdescribed with respect to FIG. 17C. In operation, as described above,the polarization of the light transmitted from the world through thefirst adaptive lens assembly 1004 is converted from a first polarizationstate to a second polarization state, e.g., from RHCP to LHCP.Subsequently, the polarization of the light transmitted through thesecond adaptive lens assembly 1008 is converted back from the secondpolarization state to the first polarization state, e.g., from LHCP toRHCP. Furthermore, as described above with respect to FIG. 11B, thelight transmitted from the world through the first adaptive lensassembly 1004 undergoes a first lens effect, e.g., converging effect,according to a first net optical power Pnet1=P1+P2 having a first sign,e.g., positive sign. Subsequently, the light transmitted through thesecond adaptive lens assembly 1008 undergoes a second lens effectopposite to the first lens effect, e.g., diverging effect, according toa second net optical power Pnet2=P1′+P2′ having a second sign, e.g.,negative sign, because the light incident on the second adaptive lensassembly 1008 has an opposite polarization as the light incident on thefirst adaptive lens assembly 1004. When Pnet1 and Pnet2 havesubstantially similar magnitudes, the overall lens effect, approximatedby P=Pnet1+Pnet2 may be substantially zero. As a result, when the useris viewing virtual content by activating the second lens assembly 1008,as well as viewing real objects in the surrounding world, the view ofthe world is relatively unaffected by the compensating effect of thefirst lens assembly 1004.

In various embodiments, when deactivated, each of the first and secondadaptive lens assemblies 1004, 1008 may provide a net optical power(positive or negative) in the range between about ±5.0 diopters and 0diopters, ±4.0 diopters and 0 diopters, ±3.0 diopters and 0 diopters,±2.0 diopters and 0 diopters, ±1.0 diopters and 0 diopters, includingany range defined by these values, for instance ±1.5 diopters.

Display Devices Including Adaptive Lens Assemblies Having a SwitchableHalf Waveplate and Waveplate Lenses

In the following, an example of a display device described supra withrespect to FIGS. 10, 11A and 11B. in which an adaptive lens assemblycomprising waveplate lenses and a switchable waveplate, e.g., theadaptive lens assembly 1300 described above with respect to FIGS.17A-17C, has been integrated, according to some embodiments. Theswitchable waveplate may be, e.g., one of broadband switchablewaveplates described above with respect to FIGS. 13A-13F, FIGS. 14A-14Cand FIGS. 15A-15B.

FIGS. 18A and 18B illustrate example display devices 1800A/1800B, eachincluding a waveguide assembly 1012 interposed between a first broadbandadaptive waveplate lens assembly 1004 and a second broadband adaptivewaveplate lens assembly 1008. The display device 1800A is similar to thedisplay device 1100A/1100B described above with respect to FIGS.11A/11B, where each of the first and second adaptive lens assemblies1004, 1008 comprises a first waveplate lens (L1/HWP1) 1704, e.g., afirst half-waveplate lens, a second waveplate lens (L2/HWP2) 1708, e.g.,a second half-waveplate lens, and a switchable waveplate (HWP3) 1712,e.g., a switchable half waveplate.

Referring to FIG. 18A, the display device 1800A in operation isdescribed, when the first and second adaptive lens assemblies 1004, 1008described above with respect to FIG. 17A are both activated. The firstand second adaptive lens assemblies 1004, 1008 may be activated when theswitchable waveplate 1712 (FIG. 17A) is activated, e.g., when no currentor voltage is applied to the switchable waveplate 1712 by the switchingcircuits 1816, 1816′. As configured, the display device 1800A may beconfigured for, e.g., displaying the real world view to the user,without displaying a virtual image. For example, the display device1800A may be configured to be used as an ordinary eyeglass or anordinary goggle, as described in detail with respect to FIG. 17B.Similar to FIG. 17A, each of first and second adaptive lens assemblies1004, 1008 include a first waveplate lens (L1/HWP1) 1804, e.g., a firsthalf-waveplate lens, a second waveplate lens (L2/HWP2) 1808, e.g., asecond half-waveplate lens, and a switchable waveplate (HWP3) 1812,e.g., a switchable half waveplate. As described with respect to FIG.17A, each of L1/HWP1 1804 and L2/HWP2 1808 may be configured to have afirst lensing effect, e.g., diverging effect, on light having a firstHCP, e.g., LHCP, passing therethrough. In addition, each of the L1/HWP11804 and L2/HWP2 1808 may also be configured to have a second lensingeffect opposite the first lensing effect, e.g., converging effect, onlight having the opposite HCP, e.g., RHCP, passing therethrough. Whendeactivated, e.g., electrically deactivated using a voltage or a currentsignal provided by the switching circuit 1816, 1816′, the HWP3 1712B(FIG. 17C) serves as a waveplate, e.g., a half waveplate. As describedabove with respect FIG. 17C, when deactivated, the HWP3 1712B (FIG. 17C)serves as a half waveplate configured to convert light passingtherethrough from light having LHCP or RHCP to light having RHCP orLHCP, respectively. On the other hand, when activated, e.g.,electrically activated using a voltage or a current signal provided bythe switching circuit 1816, 1816′, e.g., by removing the voltage or thecurrent signal, the HWP3 1712A (FIG. 17B) serves as transmitting mediumfor light without affecting the polarization. The detailed operationalprinciples of the first and second adaptive lens assemblies 1004, 1008that include the L1/HWP1 1804, L2/HWP2 1808 and HWP3, 1812A have beenprovided above with respect to FIGS. 17A and 17B, and are omittedherein.

Based on the operational principles described in detail with respect toFIGS. 17B and 17C, when the first and second adaptive lens assemblies1004, 1008 are in an activated state, the light beam (e.g., 1732A inFIG. 17B) exiting from each of the first and second adaptive lensassemblies 1004, 1008, has the same HCP as the light beam incidentthereon (e.g., 1720 in FIG. 17B). In addition, the incident light beam1720 and the exiting light beam 1732A may be substantially matched interms of the magnitudes of the lens power because of the compensation ofthe net optical powers of the first and second lens assemblies 1004,1008, as described above with respect to FIG. 13B.

FIG. 18B illustrates an example of the display device of FIG. 18A, inoperation with the switchable waveplate deactivated, according to someembodiments. The first and second adaptive lens assemblies 1004, 1008 byactivating the respective switchable waveplates 1712 (FIG. 17A), e.g.,by applying current or voltage to the switchable waveplate 1712 usingthe switching circuit 1816, 1816′. In the following, the operation ofthe display device 1800B that is outputting a virtual image to the user,while also transmitting light from an object in the real world withreduced or essentially eliminated distortion resulting from the lenseffects of the adaptive lens assemblies 1004, 1008, is described.

When displaying a virtual image, as described above with respect toFIGS. 11A and 17C, some of the light propagating in the x-directionwithin the waveguide within the waveguide assembly 1012 may beredirected, or outcoupled, in the z-direction. The light beam 1720travels, e.g., in a positive z-direction, until the light beam 1720impinges on the L1/HWP 1804 of the second adaptive lens assembly 1008.Based on the operational principles of the second adaptive lens assembly1008 described above with respect to FIG. 17C, when the second adaptivelens assembly 1008 is in an deactivated state, the exiting light beam(e.g., 1732B in FIG. 17C) has the opposite HCP as the incident lightbeam (e.g., 1720 in FIG. 17C), and is diverged according to the secondnet optical power Pnet2, for displaying the virtual content at acorresponding virtual depth plane.

In various embodiments, when deactivated, each of the first and secondadaptive lens assemblies 1004, 1008 may provide a net optical power(positive or negative) in the range between about ±5.0 diopters and 0diopters, ±4.0 diopters and 0 diopters, ±3.0 diopters and 0 diopters,±2.0 diopters and 0 diopters, ±1.0 diopters and 0 diopters, includingany range defined by these values, for instance ±1.5 diopters. In someembodiments, the first adaptive lens assembly 1004 between the waveguideassembly 1012 and the world may have a positive optical power, whereasthe second adaptive lens assembly 1008 between the waveguide assembly1012 and the user may have a negative optical power, such that theoptical powers of the first and second switchable assemblies 1004, 1008compensate each other in viewing the world.

Consequently, still referring to FIGS. 18A and 18B, the display device1800A/1800B comprise a pair of adaptive lens assemblies 1004, 1008 inthe optical path between the world 510 and the eye 210, where each ofthe pair of adaptive lens assemblies 1004, 1008 comprises a switchablewaveplate (e.g., 1712A/1712B in FIGS. 17A/17B) configured to alter apolarization state of light passing therethrough when electricallydeactivated. When electrically deactivated, the pair of adaptive lensassemblies have net optical powers (Pnet1, Pnet2) having opposite signssuch that light passing through the pair of adaptive lens assembliesconverges or diverges according to a combined optical power having amagnitude that is about a difference between magnitudes of opticalpowers the pair of adaptive lens assemblies. The virtual content may beobserved by the user at a depth plane according to Pnet2, which may benegative, while the view of the world is relatively unaffected by Pnet2that is at least partially compensated by Pnet1, which may be positive.

In some embodiments, each of the pair of adaptive lens assemblies has arespective net optical power (Pnet1, Pnet2) that is electricallyadjustable or tunable to one of a plurality of values using theswitching circuit 1816, 1816′. As described supra, as the images ofvirtual objects produced by light outcoupled by the waveguide assembly1012 move in 3D, the second net optical power (Pnet2) of the secondadaptive lens assembly 1008 on the user side is adjusted to adapt to thechanging depth of the virtual depth plane. Simultaneously, according toembodiments, the first net optical power (Pnet1) of the first adaptivelens assembly 1004 is correspondingly adjusted using the switchingcircuit 1816, 1816′, such that the view of the real world does notundesirably become defocused or distorted. To address this and otherneeds, in some embodiments, the display device 1800A/1800B comprises acontroller 1804 configured such that, when the first net optical power(Pnet1) of a first one of the pair of adaptive lens assemblies 1004,1008 is electrically adjusted, a second optical power (Pnet2) of asecond one of the pair of adaptive lens assemblies is correspondinglyadjusted, such that the combined optical power (Pnet1+Pnet2) remainsabout constant, e.g., about zero. The controller circuitry and theswitchable waveplate 1812 are configured such that the time to switchthe first and second net optical powers Pnet, Pnet2, to adjust thevirtual depth planes using the second adaptive lens assembly 1008 and tocompensate the real world view using the first adaptive lens assembly1004 as described herein, is less than about 100 milliseconds, less thanabout 50 milliseconds, less than about less than about 10 milliseconds,less than about 5 milliseconds, less than about 1 millisecond, or avalue within a range defined by any of these values.

Broadband Switchable Waveplate Lenses

As described above, according to various embodiments, broadband adaptivewaveplate lens assemblies can generate images at multiple depth planesby being selectively switched between a plurality of states havingdifferent optical powers. In some embodiments described above, thebroadband capability of the broadband adaptive waveplate lens assemblycan be enabled by one or more broadband passive waveplate lenses (e.g.,1154A in FIG. 12A) coupled with a broadband switchable waveplate (e.g.,1158 in FIG. 12A). In some other embodiments, the broadband capabilityof the broadband adaptive waveplate lens assembly can be enabled bybroadband switchable waveplate lenses without broadband switchablewaveplates (e.g., 1154B in FIG. 12B). In the following, structures andconfigurations of liquid crystal layers of broadband switchablewaveplate lenses and broadband adaptive lens assemblies having the sameare described, according to embodiments.

FIG. 19A illustrates a plan view of a broadband waveplate lens 1900comprising a layer of LC molecules formed on a transparent substrate,according to various embodiments. The spatial distribution of theelongation direction of lowermost LC molecules or the LC moleculesclosest to the substrate, and/or the local director of LC moleculesresulting therefrom, can be distributed according to the pattern ofarrows depicted in FIG. 19A. In the illustrated embodiment, the LCmolecules closest to the substrate at a given radius from a centralregion have generally the same elongation direction.

In the some embodiments, the waveplate lens 1900 is a polarization-typeFresnel zone plate (FZP) lens having a birefringence profile that isradially symmetric and radially modulated. In some embodiments, theorientation of the elongation direction of LC molecules or the localdirector can vary as a function of radius according to a mathematicalfunction. In the illustrated embodiment, the azimuthal angle φ of thelocal director of LC molecules can have discrete values in differentzones disposed at different radii from the center of the waveplate lens1900. For example, φ in the m-th zone can be expressed as

${\phi = {{\frac{\pi}{\lambda}\left( {f - \sqrt{f^{2} - r^{2}}} \right)} + {\left( {m + \frac{1}{2}} \right)\pi}}},$

where f is the focal length and r is the distance from the center of thewaveplate lens 1900.

In some other embodiments, the spatial distribution of the elongationdirection or the local directors of the LC molecules, or the localbirefringence resulting therefrom can be similar to that described abovewith respect to FIGS. 16A and 16B.

In some embodiments, local orientation directions of LC molecules, e.g.,elongation directions, above the lowermost LC molecules can be generallythe same as those of the lowermost LC molecules closest to thesubstrate. In some other embodiments, local orientation directions of LCmolecules above the lowermost LC molecules can be generally differentfrom those of the lowermost LC molecules closest to the substrate. Forexample, local orientation directions of LC molecules above thelowermost LC molecules can be successively twisted, as described infra(e.g., FIGS. 20A, 20B).

In operation, in a similar manner as the waveplate lenses describedabove with respect to FIGS. 16A and 16B, the broadband waveplate lens1900 has polarization-selective lens effect of functioning as a convex(or positive) lens (FIG. 19B) for incident light 1162B having a firstpolarization, e.g., right-handed circular polarization (RHCP), whilefunctioning as a concave (or negative) lens (FIG. 19C) for incidentlight 1162A having a second polarization, e.g., left-handed circularpolarization (LHCP). In addition, the broadband waveplate lens 1900flips the polarization of the diffracted light. That is, the incidentlight 1162B having RHCP is converted by the broadband waveplate lens1900 to light 1166A having LHCP as illustrated in FIG. 19B, while theincident light 1162A having LCHP is converted by the waveplate lens 1900to light 1166B having RHCP as illustrated in FIG. 19C. The relativeproportion of undiffracted leakage light 1904 determines the diffractionefficiency, as described above.

The inventors have found that further improvements in high bandwidthcapability of the waveplate lenses can be achieved by particularlyconfiguring the twist arrangement of LC molecules vertically within oneor more LC layers (e.g., FIGS. 20A, 20B), or by employing a negativedispersion LC material (FIG. 21), to further reduce the undiffractedleakage light 1904 and to increase the diffraction efficiency, which inturn further reduces undesirable visual effects such as ghost images, asdescribed below.

FIGS. 20A and 20B schematically illustrate plan view and cross-sectionalview of a broadband waveplate lens 2000 comprising crystal plurality ofLC layers, according to embodiments. The illustrated broadband waveplatelens 2000 comprises a stack of two LC layers 2004, 2008 having LCmolecules that have opposite twist sense, such that retardation of lightby one of the LC layers 2004, 2008 is compensated by the other one ofthe LC layers 2004, 2008. For illustrative purposes only, FIGS. 20A and20B depict the relative orientations of LC molecules that laterally varyschematically in a particular fashion. However, it will be understoodthat the lateral arrangement of the LC molecules across the x-y plane ata given depth in the z direction can have any of the variousarrangements described above, including those illustrated above withrespect to FIGS. 16A and 16B and with respect to FIG. 19A. For example,in some embodiments, the LC molecules closest to the substrate havegenerally the same local orientation direction, e.g., local elongationdirection or local director, at a given radius from the central regionand/or have orientation directions that vary as a function of radius, ina similar manner as described above with respect to FIG. 19A. Inaddition, the arrangement of LC molecules in a given columnar region inthe two LC layers 2004, 2008 can be expressed as having the nematicdirector n which varies as a function of vertical location within the LClayer according to

n(x,z)=[cos ϕ(x,z),sin ϕ(x,z),0].

where φ is the azimuth angle of the director n in the x-z plane. Thatis, for a given column of LC molecules having a first sense of twist inone of the LC layers 2004, 2008, a corresponding column of LC moleculesin the other one of the LC layers 2004, 2008 has an opposite sense oftwist. In other words, LC molecules in the two LC layers 2004, 2008 havemirror images of each of other about an interface between the two LClayers 2004, 2008.

According to embodiments, reactive mesogens can be employed to createthe arrangement of LC molecules in the two LC layers 2004, 2008. Forexample, by suitably configuring an alignment layer 1302-0, on asubstrate 1312, the bottommost LC molecules in the first LC layer 2004closest to the alignment layer 1302-0 can be arranged to have a firstazimuth angle.

The first azimuth angle can be defined, for example, according to thearrangement of elongation direction of the LC molecules as describedabove with respect to any of FIGS. 16A, 16B and 19A. In addition, the LCmolecules above the bottommost LC molecules in the first LC layer 2004can be configured to have a first twist by adding chiral agents to thefirst LC layer 2004, such that the uppermost LC molecules closest to asurface of the first LC layer 2004 has a second azimuth angle.Thereafter, by suitably configuring the surface region of the first LClayer 2004, bottommost LC molecules in the second LC layer 2008 closestto the first LC layer 2004 can be arranged to have the second azimuthangle. In addition, the LC molecules above the bottommost LC moleculesin the second LC layer 2008 can be configured to have a second chiraltwist by adding chiral agents to the second LC layer 2008, such thatuppermost LC molecules closest to the surface of the second LC layer2008 have a third azimuth angle. In some embodiments, the first andsecond chiral twist is about the same, such that the bottommost LCmolecules of the first LC layer 2004 and the uppermost LC molecules ofthe second LC layer 2008 have the same first azimuth angle.

In one example configuration, by configuring the LC layers 2004, 2008 tohave suitable thickness, e.g., between about 1 μm and 2 μm or betweenabout 1.5 μm and 2 μm, for instance about 1.7 μm, and a suitable chiraltwist between about 50 degrees and 90 degrees or between about 60degrees and 80 degrees, for instance about 70 degrees, relativebandwidth Δλ/λ₀ greater than 40%, 50% or 60%, for instance about 56% canbe achieved, within which wavelength range the diffraction efficiency isgreater than 99%, according to embodiments.

As described above, diffraction efficiency (η) can be expressed asη=sin²(πΔnd/λ), where Δn is birefringence, λ is wavelength and d isthickness. Generally, optically anisotropic materials display Δn whichdecreases with increasing λ (referred to herein as a positive dispersionof Δn). However, a positive dispersion of Δn results in different phaseretardation Γ=2πΔnd/λ, at different λ. The inventors have recognizedthat, by employing an optically anisotropic material that displays Δnwhich increases with increasing λ (referred to herein as a negativedispersion of Δn), the phase retardation Γ can be kept relativelyconstant at different λ and the diffraction efficiency η can be keptrelatively high and constant over a relatively wide wavelength range,according to embodiments.

FIG. 21 illustrates a cross-sectional view of a broadband waveplate lens2100 comprising a negative dispersion (ND) liquid crystal (LC) layer2104 formed on a substrate 1312 and an alignment layer 1312-0, accordingto embodiments. Similar to the broadband waveplate lenses describedabove with respect to FIG. 19A and FIGS. 20A/20B, to provide the lenseffect, the ND LC layer 2104 can be arranged, e.g., by suitablyarranging the alignment layer 1312-0, such that the waveplate lens 2100has a birefringence (Δn) that varies in a radial direction from acentral region. In addition, in some embodiments, the bottommost LCmolecules closest to the substrate 1312 can be arranged to generallyhave the same orientation direction at a given radius from the centralregion and to generally have orientation directions that vary as afunction of radius, in a similar manner as described above with respectto FIGS. 16A, 16B and 19A using, e.g., an alignment layer 1312-0 that issuitably configured as discussed elsewhere in the specification.

In various embodiments, the negative dispersion (ND) liquid crystal (LC)layer 2104 can have an average, a local, a mean, a median, a maximum ora minimum birefringence (Δn) of 0.05-0.10, 0.15-0.20, 0.20-0.25,0.25-0.30, 0.30-0.35, 0.35-0.40, 0.40-0.45, 0.45-0.50, 0.50-0.55,0.55-0.60, 0.60-0.65, 0.65-0.70, or a value within a range defined byany of these values. In addition, the negative dispersion (ND) liquidcrystal (LC) layer 2104 can a have a within-layer birefringence (Δn)range of 0.01-0.05, 0.05-0.10, 0.15-0.20, 0.20-0.25, 0.25-0.30,0.30-0.35, 0.35-0.40, or a value within a range defined by any of thesevalues.

Still referring to FIG. 21, unlike the LC molecules described above withrespect to FIGS. 20A and 20B, the ND LC layer 2104 may be verticallyhomogenous. For example, in the ND LC layer 2104, LC crystals formedabove the bottommost LC molecules may not be twisted. Instead, in someembodiments, within a given columnar region, the local director n may besubstantially constant across the thickness of the ND LC layer 2104. Insome other embodiments, within a given columnar region, the localdirector n may be substantially random across the thickness of the LClayer 2104.

According to various embodiments, the ND LC layer 2104 may be formed ofa material, e.g., reactive mesogens, having a material property suchthat Δn increases with increasing wavelength (λ) within at least aportion of the visible spectrum within 400-800 nm, including one or moreof a red spectrum which includes wavelengths in the range of about620-780 nm, a green spectrum which includes wavelengths in the range ofabout 492-577 nm, and a blue spectrum in the range of about 435-493 nm,or within a range of wavelengths defined by any wavelength within thevisible spectrum within about 400 nm to 800 nm, e.g., 400-700 nm,430-650 nm or 450-630 nm. In some embodiments, within any of theseranges of wavelength, the NC LC layer 2104 has a dispersion of theextraordinary refractive index n_(e) that is smaller than that of theordinary refractive index n_(o).

In some embodiments, the ND LC layer 2104 comprises smectic liquidcrystals (LC), e.g., a smectic LC-polymer composite material.

Advantageously, in some embodiments, the broadband waveplate lens 2100has a single ND LC layer 2104 having birefringence, unlike, e.g., thebroadband waveplate lens 2000 described above with respect to FIGS. 20Aand B having multiple layers.

In various embodiments of broadband waveplate lenses described abovewith respect to FIGS. 16A, 16B, 19A, 20A/20B and 21, the LC layers canbe configured to be passive or switchable, according to embodiments.When configured as a passive lens, the layer of LC molecules can beformed of polymerized LC (LCP), while when configured as a switchablelens, the layer of LC molecules can be formed of unpolymerized LCmolecules or reactive mesogens. When configured as a switchable lens,the waveplate lenses described above with respect to FIGS. 16A, 16B,19A, 20A/20B and 21 further comprises transparent electrodes on bothsides (e.g., FIG. 14C) or on the same side (e.g., FIGS. 15A/15B) of thelayer of LC molecules, in a similar manner as described above withrespect to various embodiments describe above.

FIGS. 22A-22C illustrate a switchable broadband waveplate lens 2200,which may be similar to any of the broadband waveplate lenses thatdescribed above with respect to FIGS. 16A, 16B, 19A, 20A/20B and 21, inoperation. FIGS. 22A, 22B and 22C illustrate a deactivated switchablebroadband wavelplate lens 2200 having a LHCP light beam incidentthereon, a deactivated switchable broadband wavelplate lens 2200 havinga RHCP light beam incident thereon and an activated switchable broadbandwavelplate lens 2200 having a LHCP light beam 1162A or RHCP light beam1162B incident thereon.

Referring to FIG. 22A, the switchable broadband waveplate lens 2200comprises liquid crystals arranged as described above with respect toFIGS. 16A, 16B, 19A, 20A/20B and 21 and configured to be selectivelyswitched between different lens states by electrically activating anddeactivating. In operation, the switchable broadband waveplate lens 2200is configured to diverge light according to optical power −P and toconverge light according to optical power P depending on thepolarization, e.g., circular polarization, of the incident light 1162A,1162B, according to various embodiments.

Referring to FIG. 22A, when deactivated, the switchable broadbandwaveplate lens 2200 is configured to diverge a LHCP light beam 1162Aincident thereon into a RHCP light beam 1166B according to optical power−P. Conversely, referring to FIG. 22B, when deactivated, e.g.,electrically deactivated, the switchable broadband waveplate lens 2200is configured to converge a RHCP light beam 1162B incident thereon intoa LHCP light beam 1166A according to optical power P. On the other hand,referring to FIG. 22C, when activated, e.g., electrically activated, thepolarization of the circularly polarized light passing therethrough ispreserved (not illustrated), and the RHCP light beam 1162B and the LHCPlight beam 1162A incident thereon pass through the switchable broadbandwaveplate lens 2200 without substantially being converged or diverged(i.e., optical power P˜0).

Broadband Adaptive Waveplate Lens Assemblies Having Switchable WaveplateLenses

As described above with respect to FIG. 22A-22C, a switchable broadbandwaveplate lens according to embodiments can be configured such that whendeactivated, it can exert optical powers P or −P, depending on thepolarization of the incident light, while when activated, it can exertsubstantially no optical power. The inventors have recognized that, bycombining two or more switchable broadband waveplate lenses, many morelens states can be obtained for displaying virtual images at manydifferent depths of focus. In the following, broadband adaptive lensassemblies comprising a plurality of switchable broadband waveplatelenses are described where, by configuring the broadband waveplatelenses to have different optical powers, 2^(n) different optical powerstates can be obtained for an incident light having a givenpolarization.

FIGS. 23A-23D illustrate a broadband adaptive lens assembly 2300comprising a first switchable broadband waveplate lens 2204 and a secondswitchable broadband waveplate lens 2208, each of which may operate in amanner similar to the switchable waveplate lens described above withrespect to FIGS. 22A-22C. Each of the switchable broadband waveplatelenses 2204, 2208 may be arranged in a similar manner as any of thebroadband waveplate lenses that described above with respect to FIGS.16A, 16B, 19A, 20A/20B and 21. FIGS. 23A, 23B, 23C and 23D illustratecombinations of states in which the first switchable broadband waveplatelens 2304/second switchable broadband waveplate lens 2308 aredeactivated/deactivated, deactivated/activated, activated/deactivated,and activated/activated, respectively.

In the illustrated embodiment, the first switchable broadband waveplatelens 2304 is configured in a similar manner compared to the broadbandwaveplate lens 2200 described above with respect to FIGS. 22A-22C. Thatis, when deactivated, the first switchable broadband waveplate lens 2304is configured to diverge a LHCP light beam 1162A incident thereon into aRHCP beam 1166B according to an optical power −P1. In addition, whilenot illustrated, when deactivated, the first switchable broadbandwaveplate lens 2304 is configured to converge a RHCP light beam incidentthereon into a LHCP beam according to an optical power +P1. On the otherhand, when activated, the first switchable broadband waveplate lens 2304is configured to substantially preserve the polarization of withoutsubstantially converging or diverging the circularly polarized lightpassing therethrough (i.e., optical power P1-0).

On the other hand, the second switchable broadband waveplate lens 2308is configured to operate in an opposite manner compared to the broadbandwaveplate lens 2200 described above with respect to FIGS. 22A-22C, withrespect to the sign of the optical power exerted when deactivated. Thatis, when deactivated, the second switchable broadband waveplate lens2308 is configured to converge a LHCP light beam 1162A incident thereoninto a RHCP beam 1166B according to an optical power +P2. In addition,while not illustrated, when deactivated, the second switchable broadbandwaveplate lens 2308 is configured to diverge a RHCP light beam incidentthereon into a LHCP beam according to an optical power −P2. On the otherhand, when activated, the second switchable broadband waveplate lens2308 is configured to substantially preserve the polarization of withoutsubstantially converging or diverging the circularly polarized lightpassing therethrough (i.e., optical power P2˜0).

Referring to FIG. 23A, the first switchable broadband waveplate lens2304 is deactivated and diverges the LHCP light beam 1162A incidentthereon into a RHCP light beam 1166B according to an optical power −P1.Thereafter, the second switchable broadband waveplate lens 2208 isdeactivated and diverges the RHCP light beam 1166B incident thereon intoa LHCP light beam 1170A according to an optical power −P2. In sum, theLHCP light beam 1162A incident on the broadband adaptive lens assembly2300 is diverged into the LHCP light beam 1170A according to a netoptical power of −(P1+P2).

Referring to FIG. 23B, the first switchable broadband waveplate lens2304 is deactivated and diverges the LHCP light beam 1162A incidentthereon into a RHCP light beam 1166B according to optical power −P1.Thereafter, the second switchable broadband waveplate lens 2208 isactivated and preserves the polarization of the RHCP light beam 1166Bpassing therethrough without substantially converging or furtherdiverging. In sum, the LHCP light beam 1162A incident on the broadbandadaptive lens assembly 2300 is diverged into the RHCP light beam 1166BAaccording to a net optical power of −P1.

Referring to FIG. 23C, the first switchable broadband waveplate lens2304 is activated and preserves the polarization of the LHCP light beam1162A passing therethrough without substantially converging ordiverging. Thereafter, the second switchable broadband waveplate lens2308 is deactivated and converges the LHCP light beam 1162A incidentthereon into a RHCP light beam 1170B according to optical power +P2. Insum, the LHCP light beam 1162B incident on the broadband adaptive lensassembly 2300 is converged into the RHCP light beam 1170B according to anet optical power of +P2.

Referring to FIG. 23D, the first and second switchable broadbandwaveplate lenses 2304, 2308 are both activated and preserve thepolarization of the LHCP light beam 1162A passing therethrough withoutsubstantially converging or diverging. Thus, the LHCP light beam 1162Aincident on the broadband adaptive lens assembly 2300 emergessubstantially unaffected as the LHCP light beam 1162A.

In summary, as illustrated in FIGS. 23A-23D, by selectively switchingthe first and second switchable broadband waveplate lenses 2304, 2308, abroadband adaptive lens assembly 2300 can have four different opticalpower states of 0, −P1, +P2, and −(P1+P2), according to embodiments.

In addition, while not illustrated, in an analogous manner, when theincident light is a RHCP light beam, by selectively switching the firstand second switchable broadband waveplate lenses 2304, 2308, thebroadband adaptive lens assembly 2300 can have four different opticalpower states would be 0, +P1, −P2, and +(P1+P2).

In addition, while not illustrated, in some embodiments, the secondswitchable broadband waveplate lens 2308 can be configured to operate inthe same manner as the first switchable broadband waveplate lens 2304 interms of the dependence of the sign of optical power on the polarizationof the incident light. In these embodiments, e.g., when the incidentlight is a LHCP light beam, the resulting four different optical powerstates would be 0, −P1, −P2, and −(P1−P2). In addition, if the secondswitchable broadband waveplate lens 2308 is configured to operate in thesame manner compared to the first broadband waveplate lens 2304 in termsof the dependence of the sign of optical power on the polarization ofthe incident light, when the incident light is a RHCP light beam, theresulting four different optical power states would be 0, P1, P2, and(P1−P2).

In FIGS. 23A-23D, the illustrated broadband adaptive lens assembly 2300is configured to achieve variable optical powers by independentlyswitching lenses themselves (e.g., first and second switchable broadbandwaveplate lenses 2304, 2308). However, other embodiments are possible inwhich one or both of first and second switchable broadband waveplatelenses 2204, 2208 are replaced by a combination of a passive waveplatelens and a switchable waveplate, similar to the combination of thepassive waveplate lens 1154A and switchable waveplate 1158, as describedabove with respect to FIG. 12 a.

FIG. 24A illustrates of an integrated broadband adaptive lens assembly2400 comprising a switchable layer of LC molecules similar to thosedescribed above with respect to FIGS. 19A, 20A/20B and 21, according toembodiments. The integrated broadband adaptive lens assembly 2400includes a switchable LC layer 2304, which can be similar to thosedescribed above with respect to FIGS. 19A, 20A/20B and 21, except, theswitchable LC layer 2304 is interposed between a pair of passivewaveplate lens stacks 2308, 2312. In a similar manner as described abovewith respect to FIG. 13F, LC molecules are inserted into a gap formedbetween surfaces of the passive waveplate lens stacks 2308, 2312 thatface each other by spacers 1350, which method of inserting is describedelsewhere in the specification. The first passive waveplate lens stack2308 includes a substrate 1312 on which a lower transparent electrode1316 is formed, followed by an alignment layer 2302 and a lowerpolymerized LC (LCP) layer 2302-1. Similarly, the second passivewaveplate lens stack 2312 includes a substrate 1312 on which an uppertransparent electrode 1320 is formed, followed by an alignment layer2302 and an upper polymerized LC (LCP) layer 2302-2.

Each of the first and second passive waveplate lens stacks 2308, 2312serves as waveplate lenses as well as alignment layers for aligning LCmolecules in the switchable LC layer 2304. In a similar manner asdescribed above with respect to FIG. 13F, the LC molecules of the lowerLCP layer 2302-1 closest to the gap and the LC molecules of the upperLCP layer 2302-2 closest to the gap are arranged such that the outermostLC molecules of the switchable LC layer 2304 are self-aligned, in asimilar manner as described above with respect to FIG. 13C. However,embodiments are not so limited and in some other embodiments, theoutermost LC molecules of the switchable LC layer 2204 may besufficiently aligned by the alignment layers 2302, 2302, such that oneof both of the first and second LCP layers 2302-1, 2302-2 are omitted.

In references to FIG. 24A and various embodiments throughout thespecification, a switchable LC layer, e.g., the switchable LC layer 2304inserted into the gap has a thickness of about 1 μm-50 μm, 1-10 μm,10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm or a value within any rangedefined by these values. In addition, passive LC layers, e.g., the LCPlayers 2302-1, 2302-2, can have a thickness of about 0.1 μm-50 μm, 0.1-1μm, 1-10 μm, 10-20 μm, 20-30 μm, 30-40 μm, 40-50 μm or a value withinany range defined by these values.

In the illustrated embodiment, each of the LCP layers 2302-1, 2302-2 canhave LC molecules having a net twist of 30-90 degrees, 40-80 degrees,50-70 degrees, for instance about 60 degrees.

In some embodiments, the switchable LC layer 2304 can be a single layer,similar to the LC layer described above with respect to FIG. 21.However, embodiments are not so limited. For example, the switchable LClayer 2204 can include a plurality of LC layers, in a similar manner asdescribed above with respect to FIGS. 20A/20B.

In operation, the integrated broadband adaptive lens assembly 2400described herein with respect to FIG. 24A share some characteristicsthat may be similar to the switchable waveplate 1300F described abovewith respect to FIG. 13F. For example, in both embodiments, a switchablewaveplate element (the switchable TN LC layer 1302 in FIG. 13F and theswitchable LC layer 2304 in FIG. 24A) interposed between a pair ofpassive waveplate elements (the plurality of TN LC layers 1302-1, 1302-2in FIG. 13F, the polymerized LC (LCP) layers 2302-1, 2302-2). In bothembodiments, the switchable waveplate element is configured to changethe polarization of light passing therethrough into an orthogonallypolarized light. Similarly, in both embodiments, the passive waveplateelements are similarly aligned by respective alignment layers such thatwhen the switchable waveplate element is electrically activated to passlight therethrough without diffracting, the passive waveplate elementshave cancelling effects on each other. On the other hand, when theswitchable waveplate element is electrically deactivated to diffractlight passing therethrough, the passive waveplate elements havecomplementary effects. In particular embodiments, when the passivewaveplate elements have the same optical power, and when the switchablewaveplate element is activated, the net optical power of the assembly isabout zero and the polarization of light is unaltered. On the otherhand, when the switchable waveplate element is deactivated, the netoptical power of the assembly is a net sum of the powers of theswitchable and passive waveplate elements having different signs. In thefollowing, with respect to FIGS. 24B-24D, one particular embodiment isdescribed in which the passive waveplate elements are half waveplatelenses and the switchable waveplate element is also a half waveplate.

FIGS. 24B-24D illustrate the integrated broadband adaptive lens assembly2400 in operation, which analogous to the adaptive lens assemblydescribed above with respect to FIGS. 17A-17C except, the switchablehalf waveplate in the middle is configured as a lens exerting an opticalpower.

FIG. 24B illustrates the integrated broadband adaptive lens assembly2400 described above with respect to FIG. 24A in terms of opticalfunctionality. FIG. 24C illustrates the integrated broadband adaptivelens assembly 2400A (FIG. 24A) in operation when the switchablewaveplate lens 2304 of the adaptive lens assembly 2400 illustrated inFIG. 24B is activated, whereas FIG. 24D illustrates the switchableassembly 2400B in operation when the switchable waveplate lens 2304 ofthe integrated broadband adaptive lens assembly 2400 illustrated in FIG.24B is deactivated. The integrated broadband adaptive lens assembly 2400is configured to couple and to transmit therethrough the lightoutcoupled from the waveguide assembly 1012 (FIGS. 10, 11A, 11B). Theintegrated broadband adaptive lens assembly 2400 comprises a firstwaveplate lens (L1/HWP1) 2308 corresponding to the passive waveplatelens stack 2308 (FIG. 24A), e.g., a first half-waveplate lens, a secondwaveplate lens (L2/HWP2) 2312 corresponding to the passive waveplatelens stack 2312 (FIG. 24A), e.g., a second half-waveplate lens, and aswitchable half waveplate (L3/HWP3) 2304 corresponding to the switchableLC layer 2304 (FIG. 24A).

In FIGS. 24B-24D, the L3/HWP 2304B in a deactivated state (FIG. 24D),the L1/HWP1 2308 and the L2/HWP2 2312 serve as passive half waveplatelenses configured to exert optical powers P3, P1 and P2, respectively,and to flip the handedness of a circular polarized light passingtherethrough from a first handedness (first HCP) to a second handedness(second HCP). On the other hand, the L3/HWP 2304A in an activated state(FIG. 24C) is configured to preserve the handedness of the circularpolarized light passing therethrough.

In addition, when deactivated, e.g., electrically deactivated using avoltage or a current signal provided by the switching circuit 1716, theL3/HWP3 2304B (FIG. 24D) serves as a half waveplate lens having anoptical power P3. On the other hand, when activated using the switchingcircuit 1716, e.g., by removing the voltage or the current signal, theL3/HWP3 2304A (FIG. 24C) serves as transmitting medium for light withoutaffecting the polarization or providing any substantial lensing effect.

FIG. 24C illustrates the integrated broadband adaptive lens assembly2400B in operation when the L3/HWP 2304A is activated. The integratedbroadband adaptive lens assembly 2400B may correspond to the firstadaptive lens assembly 1004 (FIG. 10, on the world side) or the secondadaptive lens assembly 1008 (FIG. 10, on the user side). By way ofexample only, integrated broadband adaptive lens assembly 2400A will bedescribed as corresponding to the first adaptive lens assembly 1004 orthe second adaptive lens assembly 1008, as part of the display device1000 (FIG. 10) that is displaying the view of the real world to the userwithout displaying a virtual image. For example, the display device 1000(FIG. 10) may be used as ordinary eyeglasses or ordinary goggles. Eachof the L1/HWP1 2308 and L2/HWP2 2312 may be configured to have a firstlensing effect, e.g., diverging effect, on light having a first HCP,e.g., LHCP, passing therethrough. While not shown, each of the L1/HWP12308 and L2/HWP2 2312 may also be configured to have a second lensingeffect opposite the first lensing effect, e.g., converging effect, onlight having the opposite HCP, e.g., RHCP, passing therethrough.

In the illustrated embodiment, the light beam 1720 may represent lightbeam from the world that is incident on either the first adaptive lensassembly 1004 (on the world side) or the second adaptive lens assembly1008 (on the user side) while the display device 1000 (FIG. 10) is beingused as ordinary eyeglasses or goggles, without displaying virtualcontent. By way of example only, the light beam 1720 having a first HCP,e.g., LHCP, travels, e.g., in a positive z-direction, until the beam1720 passes through the L1/HWP 2308, to be transmitted therethrough andconverted to a light beam 1724 having RHCP while diverging the lightbeam 1720 according to a first optical power −P1.

Still referring to FIG. 24C, subsequently, because the L3/HWP3 2304A isactivated, the light beam 1724 having RHCP transmits through the L3/HWP32304A without being substantially affected in terms of polarization orlensing effect, to be incident on the L2/HWP2 2312, as light beam 1728Ahaving RHCP. As described above, when configured as an adaptive lensassembly on the user side (e.g., second adaptive lens assembly 1004 inFIG. 10), the L2/HWP2 2312 is configured similarly as the L1/HWP1 1704(FIG. 17B), i.e., to convert the polarization and to diverge lighthaving LHCP while converging light having RHCP. Thus, the light beam1728A having RHCP is converted back to light beam 1732A having LHCP.Thus, when L3/HWP3 2304A is activated, the L1/HWP1 2308 and the L2/HWP22312 transmit light beams having opposite polarizations, such that theL1/HWP1 2308 and the L2/HWP2 2312 have opposite lensing effects on thelight passing therethrough. That is, because the light beam 1728Aincident on the L2/HWP2 2312 has RHCP, the light beam 1732A exiting theL2/HWP2 2312 is converged according to a second optical power +P2,unlike the light beam 1724 exiting the L1/HWP1 1704 that is divergedaccording to a first optical power −P1. Thereafter, upon exiting theadaptive lens assembly 1700A in the activated state, the light beam1732A may be viewed by the eye.

In some embodiments, when the L3/HWP3 2304A is activated, the firstoptical power −P1 of L1/HWP1 2308 and the second optical power +P2 ofL2/HWP2 2312 may have substantially the same or matched magnitudes whilehaving opposite signs. In these embodiments, the net optical power Pnetof the integrated broadband adaptive lens assembly 2400, which may beapproximately −P 1+P2, may be substantially zero, such that the view ofthe world is substantially unaffected to the viewer. However,embodiments are not so limited, and the first and second optical powers−P1, +P2 may have different magnitudes, such that the net optical powerPnet may have a nonzero value. For example, in some embodiments, thenonzero Pnet may be equal to an eyeglass prescription of the user,thereby allowing for corrections to focusing errors (e.g., refractivefocusing errors) of the eyes of the user.

While in the illustrated embodiment, the incident light beam 1720 hasLHCP, a similar outcome would result when the incident light beam 1720has RHCP. That is, when the light beam 1720 has RHCP, the light beams1724 and 1728A have LHCP, and unlike the illustrated embodiment, thelight beams 1724 and 1728A are converged according to an optical power+P1. Likewise, the light beam 1728A is diverged according to an opticalpower −P2, such that the net optical power Pnet may be +P1−P2, which maybe substantially zero.

It will be appreciated that the lensing effects of the L1/HWP1 2308 andL2/HWP2 2312 and the selectivity of the lensing effects to thepolarization state of incident light beams described above with respectto FIG. 24C serves as but one example, and other configurations arepossible. For example, while in FIG. 24C, the L1/HWP1 2408 and L2/HWP22312 is configured to diverge light having LHCP while converging lighthaving RHCP, in other embodiments, the L1/HWP1 2308 and L2/HWP2 2312 maybe configured to converge light having LHCP while diverging light havingRHCP.

In summary, in some embodiments, when the L3/HWP3 2304A is in anactivated state, the exiting light beam 1732A has the same HCP as theincident light beam 1720, and may be substantially matched to theincident light beam 1720 in terms of the lens effect because of thecompensation of the lens effects between P1 of L1/HWP1 2308 and P2 ofL2/HWP2 2312. As a result, when the user is not viewing virtual content,the view of the world is relatively unaffected by the presence of theadaptive lens assemblies (1004, 1008 in FIGS. 10, 11A, 11B).

FIG. 24D illustrates an example of the adaptive lens assembly of FIG.24B in operation when the L3/HWP3 2304B is deactivated. The integratedbroadband adaptive lens assembly 2400B may, e.g., correspond to thefirst adaptive lens assembly 1004 (on the world side) or the secondadaptive lens assembly 1008 (on the user side). In the following, by wayof example, integrated broadband adaptive lens assembly 2400B will befirst described as being configured as the second adaptive lens assembly1008 on the user side, as part of the display device (e.g., displaydevice 1100A in FIG. 11A) that is outputting a virtual image to theuser. Subsequently, integrated broadband adaptive lens assembly 2400Bwill be described as being configured as the first adaptive lensassembly 1004 on the world side, as part of the display device 1100B(FIG. 11B) that is simultaneously transmitting the view of the realworld while outputting the virtual image to the user, to reduce oressentially eliminate distortion of the view of the real world resultingfrom the lens effects of the second adaptive lens assembly 1008.

When configured as the second adaptive lens assembly 1008 on the userside (FIG. 11A), each of the L1/HWP1 2308 and L2/HWP2 2312 may beconfigured to diverge light having one of HCP, e.g., LHCP, passingtherethrough. Each of the L1/HWP1 2308 and L2/HWP2 2312 may also beconfigured to converge light having the other HCP, e.g., RHCP, passingtherethrough.

As described above with respect to FIG. 11A, some of the lightpropagating in the x-direction, e.g., by total internal reflection,within the waveguide assembly 1012 may be redirected, or out-coupled, inthe z-direction. The light out-coupled from the waveguide assembly 1012(FIG. 11A) may be incident on the integrated broadband adaptive lensassembly 2400B as a circularly polarized light beam 1720 having LHCP.The light beam 1720 travels, e.g., in a positive z-direction, until thelight beam 1720 is transmitted through the L1/HWP 2308 and convertedinto a light beam 1724 having RHCP while also being diverged accordingto the first optical power −P1 of the L1/HWP1 2308.

Subsequently, because the L3/HWP3 2304B is deactivated, the light beam1724 having RHCP transmitting through the L3/HWP3 2304B is converted tolight beam 1728B having LCHP while also being diverged or convergedaccording to third optical power −/+P3. Subsequently, the light beam1728B having LHCP is incident on the L2/HWP2 2312. Because, unlike thelight beam 1728A illustrated above with respect to FIG. 24C, the lightbeam 1728B incident on the L2/HWP2 2312 has LHCP, the L2/HWP2 2312further diverges the light beam 1728B according to a second opticalpower −P2 into light beam 1732B having RHCP. Thus, unlike theconfiguration illustrated with respect to FIG. 24C, the L1/HWP1 2308,the L2/HWP2 2312 and L3/HWP3 2304B in FIG. 24D can have additive lensingeffects. Thereafter, upon exiting the adaptive lens assembly 1700B inthe deactivated state, the light beam 1732A may be viewed by the eye.

In some embodiments, the first optical power −P1 of the L1/HWP1 2308 andthe second optical power −P2 of the L2/HWP2 2312 may both be negative(i.e., diverging) and may have substantially the same or matchedmagnitudes. In addition, the third optical power −P3 of the L3/HWP32304B may be negative. In these embodiments, the net optical power Pnetof the integrated broadband adaptive lens assembly 2400B, may beapproximately −(P1+P2+P3). However, embodiments are not so limited, andin some other embodiments, the third optical power +P3 of the L3/HWP32304B may be positive. In these embodiments, the net optical power Pnetof the integrated broadband adaptive lens assembly 2400B, may beapproximately −(P1+P2)+P3. In addition, the first and second opticalpowers P1, P2 may have different magnitudes.

While in the illustrated embodiment, the incident light beam 1720 hasLHCP, parallel outcome will result when the incident light beam 1720 hasRHCP. That is, when the light beam 1720 has RHCP, unlike the illustratedembodiment, the resulting light beam 1732B has LHCP and can be convergedby L1/HWP1 2308, L2/HWP2 2312 and L3/HWP3 2304B according to a netoptical power Pnet=+(P1+P2+P3).

The lensing effects of the L1/HWP1 2308, L2/HWP2 2312 and L3/HWP 2304Band the dependence of the lensing effects on the polarization state ofincident light beams described above with respect to FIG. 24D serves asbut one example, and other configurations are possible. For example,unlike in the illustrated embodiment, L1/HWP1 2308, L2/HWP2 2312 anddeactivated L3/HWP3 2304B may each be configured to converge lighthaving LHCP while diverging light having RHCP.

In the above, the integrated broadband adaptive lens assembly 2400B inthe deactivated state has been described when configured as the secondadaptive lens assembly 1008 on the user side in the display device 1100Adescribed supra with respect to FIG. 11A. As described supra withrespect to FIG. 11B, however, activating the second adaptive lensassembly 1008 to display virtual content to the user's eye 210, withoutany compensating effect, may result in a defocusing or distortion of theview of the real world, which may be undesirable. Thus, it may bedesirable to configure the first adaptive lens assembly 1004 on theworld side to at least partially compensate or negate the lens effect ofthe second adaptive lens assembly 1008 when deactivated to display thevirtual content.

Referring back to FIG. 24D, when configured as the first adaptive lensassembly 1004 (FIG. 11B) on the world side to negate the lens effect ofthe second adaptive lens assembly 1008 (FIG. 11B) on the user side,components of the adaptive lens assembly 1700B may be configuredsimilarly as described supra with respect to FIG. 11B. That is, as lighttransmitted from the world 510 to the eye 210 traverses the first andsecond adaptive lens assemblies 1004, 1008, each may be configured asdescribed above with respect to the integrated broadband adaptive lensassembly 2400B described with respect to FIG. 24D. In operation, asdescribed above, the polarization of the light transmitted from theworld through the first adaptive lens assembly 1004 is converted from afirst polarization state to a second polarization state, e.g., from RHCPto LHCP. Subsequently, the polarization of the light transmitted throughthe second adaptive lens assembly 1008 is converted back from the secondpolarization state to the first polarization state, e.g., from LHCP toRHCP. Furthermore, as described above with respect to FIG. 11B, thelight transmitted from the world through the first adaptive lensassembly 1004 undergoes a first lens effect, e.g., converging effect,according to a first net optical power Pnet1=(P1+P2+P3) having a firstsign, e.g., positive sign. Subsequently, the light transmitted throughthe second adaptive lens assembly 1008 undergoes a second lens effectopposite to the first lens effect, e.g., diverging effect, according toa second net optical power Pnet2=−(P1′+P2′+P3′) having a second sign,e.g., negative sign, because the light incident on the second adaptivelens assembly 1008 has an opposite polarization as the light incident onthe first adaptive lens assembly 1004. When Pnet1 and Pnet2 havesubstantially similar magnitudes, the overall lens effect, approximatedby P=Pnet1+Pnet2 may be substantially zero. As a result, when the useris viewing virtual content by activating the second lens assembly 1008,as well as viewing real objects in the surrounding world, the view ofthe world is relatively unaffected by the compensating effect of thefirst lens assembly 1004.

In various embodiments, when deactivated, each of the first and secondadaptive lens assemblies 1004, 1008 may provide a net optical power(positive or negative) in the range between about ±5.0 diopters and 0diopters, ±4.0 diopters and 0 diopters, ±3.0 diopters and 0 diopters,±2.0 diopters and 0 diopters, ±1.0 diopters and 0 diopters, includingany range defined by these values, for instance ±1.5 diopters.

FIGS. 25A and 25B are graphs 2500A, 2500B illustrating transmissionspectra corresponding to the integrated broadband adaptive lens assembly2400 (FIGS. 24A/24B) in which the L3/HWP3 2304 is deactivated (FIG. 24C)and activated (FIG. 24D), respectively. The simulations correspond tothe integrated broadband adaptive lens assembly 2400 in which theL3/HWP3 2304 comprises a switchable LC layer 2304 formed of anunpolymerized LC layer (e.g., the switchable LC layer 2304 in FIG. 23)of 10 μm in thickness and having Δn of 0.2, while each of L1/HWP1 2308and L2/HWP2 2312 comprises a polymerized LC layer formed of polymerizedtwisted LC molecules having a twist angle of 60 degrees (e.g., upper andlower polymerized LC (LCP) layers 2302-1, 2303-2 in FIG. 24A). Asillustrated in the graph 2500A, when the L3/HWP3 2304A is deactivated(FIG. 24C), the diffraction efficiency is high such that leakage lightis low (about 20% maximum), indicating that the incident lightefficiently diffracted by the integrated broadband adaptive lensassembly 2400A without substantially leaking through between 400 nm and800 nm. On the other hand, as illustrated in the graph 2500B, when theL3/HWP3 2304B is activated (FIG. 24D), the diffraction efficiency isvery the incident light is mostly transmitted without diffracting (about100%), indicating that the incident light is largely undiffracted by theintegrated broadband adaptive lens assembly 2400A between 400 nm and 800nm.

Chromatic Aberration Reduction in Broadband Adaptive Lens Assemblies

While having high efficiency over a wide range of wavelengths, somebroadband adaptive lens assemblies can have focal lengths or opticalpowers that substantially depend on the wavelength of light, therebyleading to significant chromatic aberration. This is because, forrelatively large focal lengths, the lens power is proportional to thecorresponding wavelength. That is, dependence of optical power P(λ) forwaveplate lenses at different wavelengths can be approximated asP(λ_(B))=P(λ_(G))λ_(B)/λ_(G) and P(λ_(R))=P(λ_(G))λ_(R)/λ_(G), where B,G, and R correspond to a wavelength in the blue spectrum, a wavelengthin the green spectrum and a wavelength in the red spectrum,respectively. Thus, there is a need to reduce chromatic aberration inbroadband adaptive lens assemblies. In the following, methods ofreducing chromatic aberration are described, according to embodiments.

In the above, e.g., with respect to FIGS. 23A-23D, embodiments ofbroadband adaptive lens assemblies having two switchable broadbandwaveplate lenses have been disclosed, which leads to 2²=4 optical powerstates for a light having a circular polarization. By extension, a stackcomprising more than two (N) switchable broadband waveplate lenses canbe formed, having 2^(N) optical power states. For example, for broadbandadaptive lens assemblies having three switchable broadband waveplatelenses (N=3), 8 optical power states can be achieved. TABLE 1illustrates calculated optical powers of a broadband adaptive assemblycomprising three switchable broadband waveplate lenses, where eachswitchable broadband waveplate lens is similar to the switchablebroadband waveplate lens described above, e.g., with respect to FIGS.22A-22C.

TABLE 1 STATE 1 STATE 2 STATE 3 STATE 4 STATE 5 STATE 6 STATE 7 STATE 8COLOR (1, 1, 1) (1, 1, −1) (1, −1, 1) (1, −1, −1) (−1, 1, 1) (−1, 1, −1)(−1, −1, 1) (−1, −1, −1) LENS 1 1 1 1 1 −1 −1 −1 −1 STATE (S1) LENS 1 11 −1 −1 1 1 −1 −1 STATE (S2) LENS 1 1 −1 1 −1 1 −1 1 −1.00 STATE (S3)BLUE 2.14 −2.14 0.43 −0.43 1.29 −1.29 1.29 −1.29 GREEN 2.50 −2.50 0.50−0.50 1.50 −1.50 1.50 −1.50 RED 3.01 −3.01 0.60 −0.60 1.81 −1.81 1.81−1.81

For a broadband adaptive assembly having three switchable broadbandwaveplate lenses, the net lens power can be expressed asP_(net)=((S₁*P₁+P₂)*S₂+P₃)*S₃, where P_(i) and S_(i)=±1(i=1, 2, 3) arethe optical powers and power states of the individual switchablebroadband waveplate lenses. For example, an activated state can berepresented as S=+1 while a deactivated state can be represented asS=−1. Referring to TABLE 1, columns labeled State 1 to State 8correspond to different lens states for each of the three lenses androws BLUE, GREEN and RED represent calculated optical powers for atwavelengths of 450 nm, 525 nm and 632 nm, respectively, that arerepresentative of blue, green and red colors of light. In thecalculation, it has been assumed that only light having onepolarization, e.g., first circular polarization reaches the eye and thatthe other is either recycled or reflected. For illustrative purposes,the optical powers of the three individual broadband waveplate lensesare calculated to be 0.5 D, 0.5 D, and 1.5 D at the green wavelength(525 nm). Based on TABLE 1, it can be seen that to obtain target netoptical powers of 0.5 D, 1.5 D, and 2.5 D, lens states 3, 5 and 1 can beselected. However, it is observed that the net optical powers at blueand red wavelengths (450 nm and 632 nm) can cause significant chromaticaberration, e.g., as large as 0.51 D, for the target net optical powerof 2.5 D for the red wavelength.

The inventors have recognized, however, that chromatic aberration can besubstantially reduced if, instead of using one state to achieve onetarget net optical power for the three colors as illustrated in TABLE 1,more than one state is used to achieve a given target net optical powerfor the different colors. This approach is illustrated in TABLE 2.

TABLE 2 STATE 1 STATE 2 STATE 3 STATE 4 STATE 5 STATE 6 STATE 7 STATE 8COLOR (1, 1, 1) (1, 1, −1) (1, −1, 1) (1, −1, −1) (−1, 1, 1) (−1, 1, −1)(−1, −1, 1) (−1, −1, −1) LENS 1 1 1 1 1 −1 −1 −1 −1 STATE (S1) LENS 1 11 −1 −1 1 1 −1 −1 STATE (S2) LENS 1 1 −1 1 −1 1 −1 1 −1 STATE (S3) BLUE2.31 −2.31 0.43 −0.43 1.63 −1.63 1.11 −1.11 GREEN 2.70 −2.70 0.50 −0.501.90 −1.90 1.30 −1.30 RED 3.25 −3.25 0.60 −0.60 2.29 −2.29 1.56 −1.56

Referring to TABLE 2, by using more than one state to achieve a giventarget net optical power for different colors, and slightly differenttarget lens powers, the chromatic aberration can be substantiallyreduced. Here, the optical powers of the three individual broadbandwaveplate lenses are 0.4 D, 0.7 D, and 1.6 D at the green wavelength(525 nm). Based on TABLE 2, it can be seen that to obtain target netoptical power of 0.5 D, a single lens state 3 can be selected. However,to reduce chromatic aberration, for a target net optical power of 1.5 D,states 5 and 7 can be selected, and for a target net optical power of2.5 D, states 1 and 5 can be selected. Compared to a chromaticaberration of 0.51 D for the target net optical power of 2.5 D shown inTABLE 1, by using more than one state for different colors, thechromatic aberration for the target net optical power of 2.5 D for thered wavelength can be reduced to 0.2.

FIGS. 26A, 26B and 26C are graphs 2600A, 2600B and 2600C illustratingcalculated target power net power versus actual net power for the blue,green and red wavelengths, respectively, illustrating the improvedchromatic aberration performance achieved by using the method of usingdifferent lens states to for different color wavelengths for achievingtarget net optical powers, according to embodiments. In each of thegraphs 2600A, 2600B and 2600C, solid black lines 2612, 2622 and 2632represent target net optical power, dotted lines 2604, 2614 and 2624represent calculated optical power when the method of using a singlelens state to obtain a given optical power as described above withrespect to TABLE 1 is used and solid gray lines 2608, 2618 and 2628represent calculated optical power when the method of using multiplelens states to obtain a given optical power as described above withrespect to TABLE 2 is used. As observed, the actual powers are closer tothe target power when multiple lens states to obtain a given opticalpower are used.

Fabrication of Broadband Waveplates and Waveplate Lenses UsingPhotoalignment

FIGS. 27A-27C illustrate an example fabrication method of a broadbandwaveplate or a broadband waveplate lens. Referring to an intermediatestructure 2700A of FIG. 27A, a transparent substrate 1312 is provided,on which an alignment layer 1302-0 is formed. The transparent substrate1312 can include, e.g., a silicon dioxide, sapphire or any suitabletransparent material. It will be understood that, while not shown,additional structures and layers may be present on the substrate 1312,leading up to the formation of the alignment layer 1302-0 according tovarious embodiments described herein. By way of example, when formingthe switchable waveplate 1300F (FIG. 13F), prior to forming thealignment layer 1302-0, a first one of the transparent electrode layers1316, 1320 may be present on the substrate 1312 prior to formation ofthe alignment layer 1302-0.

In some embodiments, the alignment layer 1302-0 can be a photo-alignmentlayer on which, when LC molecules are deposited, the LC molecules maybecome oriented along a preferential direction, for example, due toanchoring energy exerted on the liquid crystal molecule by thephoto-alignment layer. Examples of photo-alignment layers includepolyimide, linear-polarization photopolymerizable polymer (LPP),azo-containing polymers, courmarine-containing polymers andcinnamate-containing polymers, to name a few, as well as other compoundsdescribed above with respect to FIGS. 13C, 13F.

The alignment layer 1302-0 may be formed by dissolving precursors, e.g.,monomers, in a suitable solvent and coating the substrate 1312 with thesolution using a suitable process, e.g., spin coating, slot coating,doctor blade coating, spray coating and jet (inkjet) coating, amongother deposition processes. The solvent can thereafter be removed fromthe coated solution. The alignment layer 1302-0 may also be cured, e.g.,UV cured, e.g., with a polarizer, in preparation for the subsequentalignment of the LC molecules thereon.

Referring to an intermediate structure 2700B of FIG. 27B, after coatingthe alignment layer 1302-0, the alignment layer 1302-0 is opticallypatterned or recorded. The optical patterning can be performed using aholographic two-beam exposure process (FIG. 28) or an opticalreplication process using a master lens and a one-beam exposure process(FIGS. 29A, 29B).

Referring to an intermediate structure 2700C or FIG. 27C, after coatingthe alignment layer 1302-0, a LC layer 2704 is formed thereon. The LClayer 2704 may be formed by depositing on the alignment layer 1302-0 areactive mesogen mixture (including, e.g., liquid crystal monomers,solvents, photoinitiators, and surfactants) using a suitable process,including, e.g., spin coating, slot coating, doctor blade coating, spraycoating and inkjet coating, among other deposition processes.

When LC layer 2704 is integrated as part of a passive waveplate lens ora switchable waveplate, the LC layer 2704 may be cured, e.g., UV curedto photopolymerize the LC layer 2704, such that the LC molecules canbecome fixedly oriented, as described above.

In contrast, when LC layer 2704 is integrated as part of a switchablewaveplate lens or a switchable waveplate, the LC layer 2704 may befurther processed without polymerizing the LC layer 2704, such that theLC molecules can reorient themselves in response to a switching signalas described above.

Upon deposition, at least the bottommost LC molecules of the liquidcrystal (LC) layer 2704 that are immediately above the alignment layer1302-0 may be self-organized according to the configuration of thealignment layer 1302-0, depending on various applications describedherein. For example, when the LC layer 2704 forms part of a broadbandwaveplate lens, the alignment layer 1302-0 is configured such that thebottommost LC molecules have local orientations or directors that varyalong a radius of the LC layer 2704 that in a radially outward directionfrom a central region as described, e.g., with respect to FIGS. 16A,16B, 19A, as described supra. In addition, when the LC layer 2704 formspart of a broadband waveplate, the alignment layer 1302-0 is configuredsuch that the bottommost LC molecules have local orientations ordirectors that are oriented with their long axes extending generally ina first lateral direction as described, e.g., with respect to FIGS. 13A,13C. Still referring to FIG. 27C, the LC layer 2704, in someembodiments, as described elsewhere in the application, LC moleculesabove the bottommost LC molecules in the LC layer 2704 may be configuredto be arranged differently from the bottommost LC molecules in the LClayer 2704. For example, topmost LC molecules in the LC layer 2704 maybe aligned differently by a second alignment layer formed on the LClayer 2704. In addition, the LC molecules between the topmost LCmolecules and the bottommost LC molecules can have a twist, as describedwith respect to various embodiments, including FIGS. 13C and 20A/20B

After depositing the LC layer 2704 and optionally polymerizing, theintermediate structure 2700C may be further processed to form additionalstructures and/or layers, as described according to various embodimentsdescribed herein. By way of example, when forming the switchablewaveplate 1300F (FIG. 13F), after forming the LC layer 2704, theintermediate structure 2700C may be further processed to form, e.g., asecond alignment layer 1302-0 on the LC layer 2704 and a second one ofthe transparent electrode layers 1316, 1320. In addition, in someembodiments, additional LC layers may be formed on the LC layer 2704,where bottommost LC molecules of a subsequent LC layer align to topmostLC molecules of a previous LC layer, as described in FIGS. 13F and 24A.

FIG. 28 illustrate an example method of configuring an alignment layeras described above with respect to FIG. 27C for aligning LC molecules inbroadband waveplates or broadband waveplate lenses using a two-beamexposure process, sometimes referred to as polarization holography.While most conventional holography uses an intensity modulation,polarization holography involves a modulation of the polarization stateas a result of interference of light with different polarization.Referring to an intermediate structure 2800 of FIG. 28, the illustratedmethod includes forming an unpolymerized photo-alignment layer 1302-0 onthe substrate 1312, as described above with respect to FIG. 27A.Thereafter, a plurality of coherent light beams having differentpolarizations, e.g., a RHCP light beam 2808 and a LHCP light beam 2804,are directed to the alignment layer 1302-2. In the illustratedembodiment, the RHCP light beam 2808 and the LHCP light beam 2804 areorthogonal circularly polarized light beams. One of the RHCP light beam2808 and the LHCP light beam 2804, which may be a recording beam, may beconverging or diverging while other of the RHCP light beam 2808 and theLHCP light beam 2804, which may be a reference beam, may be collimating,where However, embodiments are not so limited For example, theorthogonally polarized beams can include linear vertically polarized andlinear horizontally polarized light beams or linear polarized lightbeams at ±45 degrees. In some implementations, the two-beam exposure ofthe alignment layer 1302-0 to a polarization hologram may be performedusing a UV laser (e.g., HeCd, 325 nm) with orthogonal circularpolarizations. The typical recording dose may be around a few J·cm⁻²depending on liquid crystal materials and grating parameters (e.g.,thickness d). Thereafter, a reactive mesogen mixture (including, e.g.,liquid crystal monomers, solvents, photoinitiators, and surfactants) iscoated to be aligned according to the surface pattern formed by thetwo-beam exposure, as described above with respect to FIGS. 27A-27C.

FIGS. 29A-29B illustrate an example method of configuring an alignmentlayer for aligning liquid crystal molecules in broadband waveplates orbroadband waveplate lenses by fabricating a master waveplate orwaveplate lens having a master alignment pattern of LC molecules, andusing the master waveplate or waveplate lens to replicate the masteralignment pattern of LC molecules onto a target alignment layer. Unlikethe two-beam exposure method described above with respect to FIG. 28 inwhich an interference of two orthogonally polarized light beams isemployed to directly configure the alignment layer, in the illustratedembodiment, a master waveplate lens and one polarized beam of light isused to create a similar polarization hologram in the near field. Thus,once a master lens having a master alignment pattern of LC molecules isfabricated, it can be used as a template to fabricate multiplewaveplates and waveplate lenses with a relatively simpler one beamexposure.

FIG. 29A illustrates a master waveplate or waveplate lens 2904. Themaster waveplate or waveplate lens 2904 may be fabricated using, e.g.,the processes described above with respect to FIGS. 27A-27C and 28,including forming an alignment layer using, e.g., a light interferencepattern formed by a two-beam exposure process, and thereafter forming areactive mesogen (RM) mixture layer (including, e.g., liquid crystalmonomers, solvents, photoinitiators, and surfactants) that self-alignsto the alignment layer, followed by blanket UV curing of the RM mixturelayer to polymerize the LC molecules in the RM mixture layer. FIG. 29Afurther illustrates an operational view 2900A of the master waveplate orwaveplate lens 2904, which is designed to have limited diffractionefficiency such that only a part of polarized incident light isdiffracted while passing a part unaffected. For example, in theillustrated embodiment, the master waveplate or a waveplate lens 2904 isconfigured to diffract a part (e.g., 30-70%, 40%-60%, 45-55% or anyvalue within these values, e.g., about 50%) of incident light 2908having a first polarization e.g., RHCP, into diffracted light 2912having a second polarization, e.g., LHCP, while passing part (e.g.,30-70%, 40%-60%, 45-55% or any value within these values, e.g., about50%) of the incident light 2908 through the master lens 2904 withoutdiffracting as leakage light 2916, e.g., zero order leakage light,having the same first polarization, e.g., RHCP, as the incident lightbeam 2908.

FIG. 29B illustrates an example fabrication configuration 2900B of themaster lens 2904 fabricated and configured as described above withrespect to FIG. 29A and an intermediate structure comprising analignment layer 1302-0 for aligning LC molecules in broadband waveplatesor broadband waveplate lenses. Referring to the fabricationconfiguration 2900B of FIG. 29B, the illustrated intermediate structureincludes an unpolymerized photo-alignment layer 1302-0 on the substrate1312, as described above with respect to FIG. 27A. The fabricationconfiguration 2900B includes disposed over the unpolymerizedphoto-alignment layer 1302-0 the master lens 2904. An incident lightbeam 2908 having a first polarization, e.g., a RHCP, is directed to thealignment layer 1302-2. As described above with respect to FIG. 29A,because the master waveplate or waveplate lens is designed to diffractonly a part of the incident light, upon passing through the masterwaveplate or waveplate lens 2904, two light beams having oppositepolarizations are incident on the alignment layer 1302-0. In effect, thetwo light beams incident on the alignment layer 1302-0 serve a similareffect of the two-beam exposure described above with respect to FIGS.28A, 28B. In the illustrated example, transmitted through the masterwaveplate or waveplate lens 2904 and incident on the alignment layer1302-0 are a diffracted light beam 2912 having a second polarization,e.g., LHCP, opposite the first polarization, e.g., RHCP, of the incidentlight beam 2908, and a leakage light beam 2916 having the same firstpolarization, e.g., RHCP, as the incident light beam 2908. Thus, in asimilar manner as described above with respect to FIG. 28, thediffracted light beam 2912, may be converging or diverging, may serve asa recording beam, while the leakage light beam 2916, may serve as areference beam. The interference of the diffracted light beam 2912 andthe leakage light beam 2915 causes the alignment layer 1302-0, in asimilar manner as described above with respect to FIG. 20. Thereafter, areactive mesogen mixture (including, e.g., liquid crystal monomers,solvents, photoinitiators, and surfactants) may be coated to be alignedaccording to the surface pattern formed by the two-beam exposure, asdescribed above with respect to FIGS. 27A-27C. Thus, advantageously,once the master lens 2904 is fabricated using a relatively complextwo-beam exposure method described above with respect to FIG. 28,subsequent configuration of alignment layers is performed using arelatively simple one-beam exposure as described above with respect toFIG. 29B. Advantageously, under some circumstances, the methodillustrated with respect to FIG. 29B can be performed using fullycoherent light sources, e.g., lasers, or partially coherent lightsources such as UV lamps or light emitting diodes, etc., with lessprecise optics, less vibration control and looser alignment compared tothe two-beam exposure method described above with respect to FIGS.28A-28B.

Fabrication of Broadband Waveplates and Waveplate Lenses UsingNanoimprint Alignment Layer

As described throughout the application, in various embodiments, the LCmolecules in an LC layer for broadband waveplates and waveplate lensesaccording to various embodiments can be aligned using an alignmentlayer, e.g., a photo alignment layer that can be configured using light.In other embodiments, the LC molecules can be aligned using patternednanostructures. In the following with respect to FIGS. 30A and 30B, amethod of aligning LC molecules using patterned nanostructures isdescribed, followed by an example of patterned nanostructures suitablefor serving as a waveplate lens is described with respect to FIG. 30C.

FIGS. 30A and 30B illustrate cross-sectional views of intermediatestructures 3000A, 3000B, respectively, at different stages offabrication using a nanoimprint process, according to some embodiments.

Referring to the intermediate structure 3000A of FIG. 30A, a transparentsubstrate 1312 is provided, in a similar manner as described above withrespect to various embodiments. A nanoimprint template (not shown), or ananoimprint mold, which has predefined topological patterns configuredto form an alignment pattern of LC molecules in the subsequently formedLC layer 2704 (FIG. 30B), e.g., at least the bottommost LC molecules inthe LC layer 2704 closest to the substrate 1312, is brought into contactwith a blanket base polymer layer (not shown). Subsequently, thetemplate is pressed into the blanket base polymer layer, which caninclude a thermoplastic polymer under certain temperature, e.g., abovethe glass transition temperature of the blanket base polymer layer,thereby transferring the pattern of the template into the softenedblanket base polymer layer to form an imprinted alignment layer 3004.After being cooled down, the template is separated from the imprintedalignment layer 3004, comprising an alignment pattern having predefinedtopological patterns configured to form an alignment pattern of LCmolecules in the subsequently formed LC layer 2704 (FIG. 30B). In someother approaches, after being pressed into the base polymer layer, theimprinted alignment layer 3004 is hardened by crosslinking under UVlight.

The imprinted alignment layer 3004 can include features that aresub-wavelength in dimensions. For example, the imprinted alignment layer3004 can include features having dimensions (e.g., length, width and/ordepth) of the order of a few nanometers, a few hundred nanometers and/ora few microns. As another example, the imprinted alignment layer 3004can include features having a length greater than or equal to about 20nm and less than or equal to about 100 nm. As yet another example, theimprinted alignment layer 3004 can include features having a widthgreater than or equal to about 20 nm and less than or equal to about 100nm. As yet another example, the imprinted alignment layer 3004 caninclude features having a depth greater than or equal to about 10 nm andless than or equal to about 100 nm. In various embodiments, the lengthand/or width of the features can be greater than the depth of thefeatures. However, in some embodiments, the depth can be approximatelyequal to the length and/or width of the features. The features of eachdomain of the imprinted alignment layer 3004 can be arranged to formcomplex geometric patterns within each domain in which the directionand/or the period between consecutive features changes along lengthscales of the order of a few nanometers, a few hundred nanometers and/ora few microns.

While an example process of nanoimprinting was described for forming thenanoimprinted alignment layer 3004 with respect to FIG. 30A, embodimentsare not so limited. In other embodiments, the imprinted alignment layer3004 can be fabricated using other patterning techniques includinglithography and etch. In addition, while the imprinted alignment layer3004 was described as being formed of a polymeric material, embodimentsare not so limited and in various other embodiments, the imprintedalignment layer 3004 can comprise a dielectric material, e.g., siliconor a glass material.

Referring to the intermediate structure 3000B of FIG. 30B, after formingthe alignment layer 3004, an unpolymerized LC layer 2704, e.g., a layerof reactive mesogens, is deposited thereon, according to the depositionprocess described above with respect to FIGS. 27A-27C. Without beingbound to any theory, the imprinted alignment layer 3004 serves as analignment layer that causes the LC molecules of the LC layer 2704 toalign according to the pattern of the imprinted alignment layer 3004.For example, the elongation direction of LC molecules within a domainmay generally align in a direction parallel to the local elongationdirection of the nanostructures in the imprinted alignment layer 3004.Without being bound to any theory, the alignment of the LC molecules tothe pattern of the imprinted alignment layer 3004 may be attributed tosteric interactions with the liquid crystal molecules, and/or anchoringenergy exerted on deposited LC molecules by the imprinted alignmentlayer 3004.

Still referring to the intermediate structure 3000B of FIG. 30B, the LClayer 2704 may be further processed according to different embodiments,as described above with respect to FIGS. 27A-27C, includingpolymerization, further aligning LC molecules above the bottommost LCmolecules and stacking multiple LC layers.

FIG. 30C illustrates a plan view of a nanoimprinted alignment layer 3004that is fabricated according to the method described above with respectto FIGS. 30A-30B. The imprinted alignment layer 3004 can serve as analignment layer to form a layer of LC molecules having various lateralarrangements as described herein including, e.g., the arrangementsdescribed above with respect to FIGS. 13A, 13C, 16A, 16B, 19A, 40, 41,among other arrangements.

When LC layer resulting from the imprinted alignment layer 3004 formspart of a waveplate lens, the imprinted alignment layer 3004 accordingto various embodiments comprises a plurality of zones such as, forexample, concentric zones 3008-1, 3008-2, . . . 3008-n in the x-y plane,according to various embodiments. The imprinted nanostructures withineach of the zones of the imprinted alignment layer 3004 are orientedalong a particular orientation. The orientation of the molecules of theliquid crystal material in adjacent zones can be different. For example,the elongated directions or the local directors of the LC molecules inthe various zones zone 3008-1, 3008-2, . . . 3008-n can be successivelyrotated in a radial direction according to a function that depends on apower of the radius r^(n) from a central location, where n can vary fromabout 1 to 3 as described, for example, with respect to FIGS. 16A/16Band FIG. 19.

The imprinted nanostructures and the resulting liquid crystal moleculescan have elongation directions that are different in different zones3008-1, 3008-2, . . . 3008-n. For example, the elongation direction ofimprinted nanostructures in successive zones can be rotated in aclock-wise direction by an angle of about 18 degrees with respect eachother. However, embodiments are not so limited and the relative rotationangle between successive zones can be less than 1 degree, between about1 and 45 degrees, between about 1 and 18 degrees, or between about 18and 45 degrees.

Integration of Broadband Adaptive Lens Assemblies Having BroadbandWaveplates and/or Waveplate Lenses

According to various embodiments described above, e.g., broadbandadaptive lens assemblies include integrated waveplates and waveplatelenses. In the following, methods of integrating the waveplates andwaveplate lenses are described, according to embodiments. FIGS. 31A-31Cillustrate an example method of fabricating a switchable broadbandwaveplate comprising liquid crystals or a switchable broadband waveplatelens comprising liquid crystals using a gap fill process. According tovarious embodiments, the method includes providing a lower stackincluding a first electrode layer on a first substrate and a firstalignment layer formed on the first electrode layer, and includesproviding an upper stack including a second electrode layer on a secondsubstrate and a second alignment layer formed on the second electrodelayer. The first and second stacks are then stacked into a single stack,such that the first and second alignment layers face each other, wherespacers are formed between the lower and upper stacks to create a gaptherebetween, which gap is subsequently filled with a liquid a LC layermaterial.

Referring to FIG. 31A, the method includes providing a substrate 1312 ina similar manner as described above, e.g., with respect to FIG. 27A, andthereafter forming on the substrate 1312 a first electrode layer 1320,e.g., a transparent electrode layer, in a similar manner as describedabove, e.g., with respect to FIG. 27A. Thereafter, referring to FIG.31B, a first alignment layer 1302-0 is formed on the substrate 1312,thereby forming a lower stack 3100A. The alignment layer 1302-2 can be aphoto-alignment layer similar to that described above with respect to,e.g., FIGS. 27A-27C, 28 and 29, or an imprinted alignment layer similarto that described above with respect to, e.g., FIGS. 30A-30C.

Referring to FIG. 31C, in a similar manner as forming the lower stack3100A, an upper stack 3100B is formed, comprising a second substrate1312 on which a first electrode layer 1320, e.g., a transparentelectrode layer, and a second alignment layer 1302-0 is formed in asimilar manner as described above with respect to forming the lowerstack 3100A, as described above with respect to FIG. 31B.

In some embodiments, the first and second alignment layers 1302-0, whichmay be photo-alignment layers or imprinted alignment layers, may beconfigured differently, as described above with respect to variousembodiments, such that LC molecules immediately adjacent the first andsecond alignment layers 1302-0 align differently, e.g., align such thatthe elongation direction or the director direction of the LC moleculescross each other, e.g., at about 90 degrees.

Still referring to FIG. 31C, the upper and lower stacks 3100B, 3100A aresubsequently stacked into a single stack, such that the first and secondalignment layers 1302-0 face each other, where a gap 1302 is formedtherebetween. The gap 1302 may be formed by spacers 1350 formed betweenthe lower and upper stacks 3100A, 3100B.

The spacers 1350 may be formed of a suitable material, e.g., silicabeads having a diameter to produce the gap, whose distance defines thetarget thickness of the subsequently inserted LC material. In someimplementations, the spacers 1350 in the form of silica beads, can bedispersed using a dry process over the surface of one or both of theupper and lower stacks 3100B, 3100A. In other implementations, thespacers 1350 in the form of silica beads can be mixed with adhesives andapplied at the edges of the surfaces of one or both of the upper andlower stacks 3100B, 3100A. Thereafter, upper and lower stacks 3100B,3100A are pressed against each other, until a final gap distancecorresponding to the resulting thickness of the LC layer, is obtained.The gap distance can be monitored using a Fabry-Perot interferencefringes.

After forming the gap 1302, a LC material is inserted into the gap 1302.The inserted LC material can be a reactive mesogen mixture including,e.g., liquid crystal monomers, solvents, photoinitiators, andsurfactants, as described above. The LC material may be inserted in thegap 1302 by capillary force. In some implementations, the insertion isperformed under vacuum.

The integration process described above with respect to FIGS. 31A-31Ccan be applied to any suitable embodiment described herein. For example,the method can be used to form a switchable broadband waveplate similarto that described above with respect to FIG. 13F, including a pair ofbroadband QWP 1324, 1326 (FIG. 13F) separated by the switchable TN LClayer 1302 (FIG. 13F) inserted into the gap 1302 as described above. Inthese embodiments, the lower stack 3100A includes a plurality of TN LClayers 1302-1, 1302-2 (FIG. 13F) that are configured to serve as a QWP1324 (FIG. 13B), and the upper stack 3100B similarly includes aplurality of TN LC layers 1302-1, 1302-2 (FIG. 13F) that are configuredto serve as a QWP 1326 (FIG. 13B).

To provide another example, the integration process described above withrespect to FIGS. 31A-31C can be applied to form an integrated broadbandadaptive lens assembly similar to that described above with respect toFIG. 24A, including a pair of polymerized LC (LCP) layers 2302-1, 2302-2(FIG. 24A) separated by the switchable LC layer 2304 (FIG. 24A) insertedinto the gap 1302 as described above to serve as the L3/HWP3 2304 (FIGS.23B-24D). In these embodiments, the lower stack 3100A includes the lowerpolymerized LC (LCP) layer 2302-1 (FIG. 24A) that serves as a L1/HWP22308 (FIGS. 24B-24D), and the upper stack 3100B similarly includes theupper polymerized LC (LCP) layer 2302-2 (FIG. 24A) that serves as aL2/HWP2 2312 (FIGS. 24B-24D).

In the following, methods of integrating the waveplates and waveplatelenses are described, according to some other embodiments. In FIGS.32A-32E, an example method of fabricating a switchable broadbandwaveplate comprising liquid crystals or a switchable broadband waveplatelens comprising liquid crystals employs a layer transfer process. In thelayer transfer process, a LC layer is formed on a donor, a sacrificialor a carrier substrate, which may be flexible, and thereafter betransferred to a permanent substrate, which may be rigid. The LC layerformation on such a carrier substrate may allow for higher manufacturingthroughput and/or higher manufacturing yield.

FIG. 32A illustrates an intermediate structure 3200A comprising acarrier substrate 3204, which may be a suitable substrate havingsufficient flexibility while having sufficient thermal stability forsubsequent processes including polymerization of a LC layer, on which analignment layer 1302-0 is formed. The alignment layer 1302-0 can be aphoto-alignment layer formed and configured in a similar manner to thosedescribed above with respect to, e.g., FIGS. 27A-27C, 28 and 29, or animprinted alignment layer formed and configured in a manner similar tothat described above with respect to, e.g., FIGS. 30A-30C.

FIG. 32B illustrates an intermediate structure 3200B comprising arelease layer 3208 formed on the alignment layer 3208 and FIG. 32Cillustrates an intermediate structure 3200C comprising an LC layer 3212formed on the release layer 3208, thereby temporarily bonding the LClayer 3212 on the alignment layer 3208. The LC layer 3212 can be formedand configured in a similar manner as describe above with respect toFIG. 27C.

In some embodiments, the release layer 3208 comprises a thin surfacelayer formed by a surface treatment which weakens the adhesion strengthbetween the LC layer 3212 and the alignment layer 1302-0 withoutsubstantially affecting the alignment properties of the alignment layer3208.

In some embodiments, the release layer 3208 is a separate suitable thinfilm that is coated on the alignment layer 1302-0 which adheres with ahigher strength to the layer below compared to the layer above therelease layer 3208. In the illustrated example, the release layer 3208is formed between the alignment layer 1302-0 and a LC layer 3212 (FIG.32C). Thus, according to some embodiments, release layer 3208 is formedof a suitable material that forms a stronger adhesion interface with thealignment layer compared the LC layer 3212, such that it separatesrelatively easily from the LC layer 3212 compared to the alignment layer3202-2, upon application of a mechanical force

In some embodiments, the release layer 3208 comprises a separateliquid-like curable adhesive coated on the release layer 3208 that canbe cured in place when exposed to UV light for curing the LC layer 3212.Curing converts the adhesive layer into a 3-D polymer network that isresistant to flow prior to separation. In some other embodiments, therelease layer 3208 comprises a separate thermoplastic bonding materialcoated on the release layer 3203 rather than a curable adhesivematerial. Thermoplastic bonding material comprises thermoplasticpolymers that do not crosslink or cure but instead reversibly soften andthen re-harden to a glassy state when cooled to room temperature. Atroom temperature, the thermoplastic bonding material forms a stiff,resilient bond that allows subsequent processes without substantialdeformation.

FIG. 32D illustrates an intermediate structure 3200D comprising a targetsubstrate 1312, which may be a permanent substrate, attached on the LClayer 3212 using a glue layer 3216. The substrate 1312 may be anytransparent substrate described elsewhere in the specification.

FIG. 32E illustrates an intermediate structure 3200 e in which a targetstack including the target substrate 1312 attached to the LC layer 3212by the glue layer 3216 is separated from a carrier stack including thecarrier substrate 3204, the alignment layer 1302-0 and the release layer3208. In some embodiments, the separation is performed by a mechanicaldebonding, which is sometimes called peel separation. The separationoccurs at an interface between the release layer 3208 and the LC layer3212, e.g., at the surface-treated release layer 3208 or one ofdifferent types of separately deposited release layers described above.The separate release layer 3208 or the surface treatment are designed tohave sufficient adhesion at their interface that the bonded structurecan survive normal in-process stresses but not be so strongly bondedthat a strong force, which could break the thin device wafer, is neededto separate between the layers. The separation process can involveinitiating a delamination between the release layer 3208 and the LClayer 3212 at an edge interface, which propagates across the entireinterface between the release layer 3208 and the LC layer 3212 usingvery low force to cause separation. The use of a thermoplastic bondingmaterial and a low-surface-energy polymeric release layer, which can bea curable or thermoplastic composition, can be suitable for mechanicaldebonding. However, embodiments are not so limited and in some otherembodiments, separation involves slide debonding. These embodiments takeadvantage of the reversible softening behavior of thermoplastic bondingmaterials. In this mode, the bonded structure is heated above thesoftening temperature of the bonding material and an opposing shearforce is applied to the device and carrier wafers, causing them toslowly slide past one another until the structure is separated. In yetsome other embodiments, separation involves laser debonding. In theseembodiments, a laser beam is used to ablate, or decomposes the releaselayer 3208 into gaseous byproducts and a small amount of carbonaceousresidue, when irradiated through the carrier substrate 3204 with ascanning laser.

Still referring to FIG. 32E, the LC layer 2704 on the thus separatedtarget stack can be further processed, may be further processedaccording to different embodiments, as described above with respect toFIGS. 27A-27C, including polymerization, further aligning LC moleculesabove the bottommost LC molecules and stacking multiple LC layers.

Formation of Broadband Adaptive Lens Assemblies on Selected SubstrateAreas

As described above with respect to various display devices, e.g., thewearable display device 1000 (FIG. 10), broadband adaptive lensassemblies e.g., a pair of broadband adaptive lens assemblies 1004, 1008can be formed in an optical path 1016 that are interposed by a waveguideassembly 1012 for displaying both virtual and world images. However, insome implementations as a part of a wearable display device, thebroadband adaptive lens assemblies may be formed on a portion of asubstrate, e.g., on a portion of the waveguide assembly 1012 or aportion of a lens of goggles where they eye 210 is expected to viewvirtual images. In the following, various embodiments of formingbroadband adaptive lens assemblies on selected substrate areas aredescribed.

FIG. 33 illustrates an example of a switchable broadband waveplatecomprising liquid crystals or a switchable broadband waveplate lenscomprising liquid crystals formed on a portion of a substrate 3300. Thesubstrate 3300 may represent, e.g., a portion of the waveguide assembly1012 or a portion of a lens of the wearable display device 1000 (FIG.10) such as goggles or eyeglasses. The substrate 3300 comprises a lensarea 3204 on which an optically active switchable broadband waveplate orswitchable broadband waveplate lens is to be formed, and a clear region3308 which is to remain free of the switchable broadband waveplate orthe switchable broadband waveplate lens.

FIG. 34 illustrates a first example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate3400 by selectively coating or depositing a LC layer 3404 of theswitchable broadband waveplate or the broadband waveplate lens on thelens area 3204 while preventing their formation in the clear area 3308.The LC layer 3404 may be first coated in the form of a reactive mesogenmixture layer (including, e.g., liquid crystal monomers, solvents,photoinitiators, and surfactants) as described above with respect toFIGS. 27A-27C, followed by suitable subsequent processes, e.g., solventevaporation and optional polymerization (for polymerized LC layers). Insome embodiments, the selective coating can be performed using asuitable non-contact or contact process for depositing each layer, suchas slot-die coating process, Gravure coating process or jet (ink-jet)coating process.

FIGS. 35A-35C illustrates an example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate byblanket coating a layer of liquid crystals and subtractively removing.Referring to FIG. 35A, a reactive mesogen layer 3504 (which may include,e.g., liquid crystal monomers, solvents, photoinitiators, andsurfactants) is initially formed over an entire area of the substrate3300 (FIG. 33) in a similar manner as described above with respect toFIGS. 27A-27C, followed by suitable subsequent processes, e.g., solventevaporation. Thereafter, referring to FIG. 35B, the reactive mesogenlayer in the lens region 3304 is selectively cured using an optical maskor a reticle to block the UV light in the clear region 3308, such that apolymerized LC layer 3508 is formed in the lens region 3304 while anuncured reactive mesogen layer 3512 remains in the clear area remainsuncured (i.e., unpolymerized). Subsequently, referring to FIG. 35C, theuncured reactive mesogen layer 3512 is selectively removed from theclear region 3308 using a suitable solvent, resulting in a selectivelycoated substrate 3500C having the polymerized 3508 selectively remainingonly in the lens region 3304.

FIG. 36A-36C illustrates an example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate byusing selective optical patterning of an alignment layer. Referring toan intermediate structure 3600A illustrated in FIG. 36A, afterblanket-depositing a photo-alignment layer, a first optical mask or areticle 3604 is used to cover the lens area 3304 while exposing theclear region 3308 to uniform linearly polarized light. Thereafter,referring to an intermediate structure 3600B illustrated in FIG. 36B,using a second optical mask or a reticle 3616 which may be have aninverse mask pattern relative to the first optical mask 3604, the lensarea 3304 is exposed to a polarization hologram using, e.g., thetwo-beam exposure process using orthogonally polarized UV laser beamsdescribed above with respect to FIG. 29, while the clear region 3308 iscovered. As described above with respect to FIGS. 28 and 29A/29B, aninterference of light having orthogonal polarizations causes thealignment layer to be configured to align the LC crystal moleculessubsequently formed thereon according to a waveplate pattern or awaveplate lens pattern described with respect to various embodimentsdescribed above. Thus, as a result of the arrangements of the first andsecond optical masks 3604, 3616, the portion of the alignment layer 3616(FIG. 36B) in the lens area is selectively configured to align LCmolecules subsequently formed thereon. In contrast, the portion of thealignment layer 3608 (FIG. 36A) in the clear area is configureddifferently and lacks a waveplate pattern or a waveplate lens patterndescribed with respect to various embodiments described above.Thereafter, referring to an intermediate structure 3600C illustrated inFIG. 36C, reactive mesogen layer 3620 (which may include, e.g., liquidcrystal monomers, solvents, photoinitiators, and surfactants) is blanketdeposited over an entire area of the substrate including the clearregion and lens area, in a similar manner as described above withrespect to FIGS. 27A-27C, followed by suitable subsequent processesincluding, e.g., solvent evaporation and optional UV curing. In theresulting intermediate structure 3600C in FIG. 36C, while the entiresurface area is covered with LC molecules, the LC molecules over thelens area are aligned according to the configuration of the underlyingalignment layer and have systematic orientations to serve as a waveplateor a waveplate lens according to various embodiment s described above,while the LC molecules over the clear region lack systematicorientations to serve as a waveplate or waveplate lens.

FIG. 37A-37B illustrates an example method of forming a switchablebroadband waveplate comprising liquid crystals or a switchable broadbandwaveplate lens comprising liquid crystals on a portion of a substrate byusing selective nanoimprinting an alignment layer. Referring to anintermediate structure 3700A illustrated in FIG. 37A, a nanoimprintedalignment layer is formed over the substrate surface, where thenanoimprinted alignment layer has different patterns between the lensarea 3304 and the clear region 3308. In particular, the portion of thenanoimprinted alignment layer 3708 (FIG. 37A) in the lens area 3304 isconfigured to align the LC crystal molecules subsequently formed thereonaccording to a waveplate pattern or a waveplate lens pattern describedwith respect to various embodiments described above. In contrast, theportion of the lens alignment layer 3608 (FIG. 37A) in the clear area isconfigured differently and lacks a waveplate pattern or a waveplate lenspattern described with respect to various embodiments described above.Subsequently, referring to an intermediate structure 3700B illustratedin FIG. 37B, a reactive mesogen layer 3712 (which may include, e.g.,liquid crystal monomers, solvents, photoinitiators, and surfactants) maybe blanket deposited over both the clear region 3308 and the lens area3304, in a similar manner as described above with respect to FIGS.27A-27C, followed by suitable subsequent processes including, e.g.,solvent evaporation and optional UV curing. In the resultingintermediate structure 3600C, while the entire surface area is coveredwith LC molecules, the LC molecules over the lens area 3304 are alignedaccording to the configuration of the underlying imprinted alignmentlayer and have systematic orientations to serve as a waveplate or awaveplate lens according to various embodiment s described above, whilethe LC molecules formed over the clear region 3308 lack systematicorientations to serve as a waveplate or waveplate lens.

Polarization Switches Configured to Provide Wide Field of View

A wide variety of examples of adaptive lens assemblies comprisingwaveplate lenses and switchable waveplates receiving light from a widefield-of-view are discussed above. As described above with reference toFIGS. 13A-13F, various implementations of such adaptive lens assembliesmay include one or more layers of twisted nematic (TN) liquid crystal(LC) molecules. The efficiency at which the switch converts from a firstpolarization state to a second polarization state of TN LC molecules,however, depends at least in part on the angle at which light isincident thereon. As such, increasing the angle of incidence of light ona TN LC layer (e.g., in a switchable waveplate) may cause a reduction inthe ability to alter, e.g., rotate, the polarization state of theincident light. This characteristic may cause light directed fromobjects widely off-axis in the field of view to be effected differentlythan light propagating directly down an optical axis of the adaptivelens assembly normal to the switchable waveplate and waveplate lens.

FIG. 38 illustrates an example of an adaptive lens assembly 3800comprising a liquid crystal lens (e.g., waveplate lens) 3802 such as aliquid crystal (LC) diffractive lens and a polarization switch orswitchable waveplate (e.g., switchable waveplate including at least onelayer of TN LC molecules) 3804 receiving light from a widefield-of-view. Light from objects 3808 on or near the periphery 3810 ofthe field-of-view are shown incident on the switchable waveplate 3804 atan angle, θ. This angle of incidence, θ, is measured with respect to anormal 3812 to the switchable waveplate 3804. The polarization switch3804 may be configured such that when the polarization switch is in onestate, the polarization switch or switchable waveplate 3804 rotates thepolarization of light incident thereon. For example, right handedcircularly polarized (RHCP) light incident on the polarization switchsuch as the switchable waveplate 3804 may be rotated into left handedcircular polarized (LHCP) light. Such effect may, for example, occur forlight incident on the polarization switch or switchable waveplate 3804at normal incidence thereto. Light having a larger angle of incidence,θ, may not completely be converted from right handed polarized light toleft hand polarized light.

Accordingly, light from off-axis objects 3808, for example, in theperiphery 3810 of the field-of-view that is incident on the polarizationswitch or switchable waveplate 3804 at an angle, θ, greater than zero,may not experience complete conversion of the polarization (e.g., fromright hand circularly polarized light to left hand circularly polarizedlight). The result may be non-uniform treatment of light directed fromdifferent regions of the field-of-view onto the polarization switch 3804and adaptive lens assembly 3800. The adaptive lens assembly 3800 mayconsequently produce ghost images at the wrong depth plane when such anelement is used as a variable focus element for an augmented realitydevice. Therefore, there is a need to increase the field-of-view of theswitchable waveplate 3804 as shown in FIG. 38.

FIG. 39 shows an example of this non-uniformity. FIG. 39 is a plot 3900that illustrates the efficiency at which an example LC layer of theswitchable waveplate 3804 converts polarization at different angles oflight incident thereon. This contour plot plots the simulated percentageof light leaking through parallel circular polarizers with anelectrically-controlled birefringence (ECB) LC cell in between. An ECBLC cell is a simple switchable waveplate, where the LC molecules are allaligned parallel in the same direction, e.g., along x-axis in thecoordinate system shown. Typically the thickness of the LC layer (d) ischosen such that Δn*d=λc/2, where Δn is the LC birefringence, and λc isthe center wavelength. When no external voltage is applied, this LC cellcan convert right handed circularly polarized light into left handcircularly polarized light, and vice versa. The amount of conversion canbe measured as the percentage (%) of light leakage through parallelcircular polarizers over the field-of-view. The coordinate system is apolar coordinate system that maps polarization conversion or rotationefficiency for different angles of incident light on the polarizationswitch or switchable waveplate 3804. The center 3906 corresponds tolight normally incident on the polarization switch or switchablewaveplate 3804, for example, along a central or optical axis through thepolarization switch or switchable waveplate. Azimuthal angles of 45,135, 225, and 315 degrees are marked. The polar grid also has circles3908 a, 3908 b, and 3908 c representing 10, 20, and 30 degrees ofelevation angle with respect to the central axis or optical axis throughthe example TN LC layer of the polarization switch or switchablewaveplate 3804.

Substantially dark regions 3902 in the plot 3900 shows that, for much ofthe light at different angles, the polarization is efficiently convertedor rotated. However, some light regions 3904 of the plot shows that, forsome of the light at higher angles corresponding to less central regionsof the field-of-view, the polarization is not as efficiently convertedor rotated. Various polarization switches or switchable waveplatedesigns disclosed herein are configured to provide more efficientpolarization conversion/rotation for various high angles correspondingto more peripheral locations 3810 in the field-of-view.

FIG. 40 illustrates a design for a switchable waveplate 4204 configuredto increase the efficiency of polarization rotation or conversion forlight from objects on or near the periphery 4210 of the field-of-view.The switchable waveplate 4204 includes a liquid crystal layer comprisingmolecules 4205 that are rotated about respective local axes 4201 thatare parallel to a central axis 4224 through the switchable waveplate. Asshown, the local axis 4201 go through the center of the liquid crystalmolecule and are parallel to the central axis or optical axis 4224. Theamount of rotation of the molecule 4205 is represented by an angle, φ.This rotation depends on the location of the molecule 4205. Inparticular, the orientation of the molecules 4205 varies with azimuthalangle, Φ, about the central axis 4224 corresponding to the location ofthe molecule with respect to the central axis. As a result, in theillustrated implementation, the elongated molecules are generallyarranged along concentric rings 4203 about the central axis 4224. Thisconfiguration potentially increases the uniformity in efficiency ofpolarization rotation of the switchable waveplate 4204 even for highlyoff-axis field-of-view angles.

FIG. 40, in particular, shows an example of an adaptive lens assembly4200 comprising a liquid crystal lens (e.g., waveplate lens) 4202 suchas a liquid crystal (LC) diffractive lens and the polarization switch(e.g., switchable waveplate) 4204, wherein the switchable waveplate isflat or planar. The polarization switch or switchable waveplate 4204 hasfirst and second surfaces (e.g., outer and inner surfaces) and a liquidcrystal layer disposed therebetween. The first and second surface, inthis example, are flat or planar. Light from objects 4208 on or near theperiphery 4210 of the field-of-view is illustrated as being incident onthe switchable waveplate 4204.

FIG. 40 illustrates the liquid crystal layer comprising a plurality ofliquid crystal molecules 4205 that are rotated about local axes 4201parallel to the central axis or optical axis 4224. These molecules arerotated about the local axes 4201 by respective angles, φ, with respectto a reference 4215 such as the horizon. The local axes 4201 areillustrated as parallel to the z-axis in FIG. 40. Likewise, the angularrotation, φ, is in a plane parallel to the x-y plane. Similarly, invarious implementations, the angular rotation, φ, is in a plane parallelto the first and second surfaces. This rotation can be referred to asazimuthal rotation about respective the local axis 4201 for the molecule4205 (e.g., intersecting the center of the molecule) that is parallel tothe central axis 4224.

The liquid crystal molecules 4205 are positioned at different locationsabout the central axis 4224. Accordingly, an azimuthal angle, Φ, may beused to specify the location, for example, in polar coordinates of theparticular molecule 4205 with respect to the central axis 4224. Invarious implementations of the switchable waveplate 4204, such as theimplementation shown in FIG. 40, the liquid crystal molecules 4205 arerotated about the respective local axes 4201 passing through themolecule by an angular (e.g., azimuthal) rotation, φ. This rotation isby an amount that varies depending on the position of the molecule. Inparticular, the amount of rotation depends on the azimuthal angle, Φ,corresponding to the location, for example, in polar coordinates of theparticular molecule with respect to the central axis 4224. Accordingly,in various implementations, the liquid crystal molecules 4205 aregenerally longer than wide along a longitudinal direction 4232.Additionally, the plurality of liquid crystal molecules 4205 are rotatedabout the respective local axes 4201 parallel to the central axis 4224such that the molecule has a side elongated along the longitudinaldirection 4232 that faces the central axis. As a result, in variousimplementations, the molecules have a particular spatial arrangement. Invarious implementations, for example, the molecules 4205 form concentricrings 4203 about the central axis 4224 of the switchable waveplate 4204.The molecules may be arranged in these rings 4203 such that theelongated sides of the molecules 4205 may face the central axis 4224 invarious implementations. In certain implementations, the molecules 4205in a particular ring 4203 have a radial distance from the central axisor optical axis 4224 that is the same. For different rings 4203,however, the radial distances of the molecules 4205 from the centralaxis 4224 is different. In some implementations, the plurality of liquidcrystal molecules 4205 are rotated about the local axes 4201 parallel tothe central axis 4224 such that longitudinal direction 4232 isorthogonal to a radial direction from the central axis to the center ofthe molecule.

This spatial arrangement of the molecules may result in the polarizationconversion or rotation being more uniform across the polarization switch4204 as compared to a spatial arrangement where the molecules areoriented in the same direction for all locations (e.g., all vertical orall horizontal). The polarization conversion or rotation of lightincident along the central axis 4224 (e.g., optical axis) through thepolarization switch 4204 (e.g., through the first and second surfacesand the liquid crystal layer) may, for example, be similar to thepolarization conversion or rotation for off-axis light coming fromobjects 4208 located at the periphery 4210 of the field-of-view. Thisresult may be a consequence of the rotated orientation of the individualliquid crystal molecules 4105, which increases the likelihood that theangle of incidence of light from different objects 4108 in thefield-of-view is substantially the same. The approach taken in FIG. 40follows from the deficiencies found in the liquid crystal layer of FIG.39. When the plane of incidence is close to either the LC alignmentdirection or perpendicular to it, the polarization conversion isrelatively high even for high incident angles, thereby effectivelycausing the polarization conversion across the polarization switch 4204to operate within the substantial dark regions 3902 or low leakageregions along the 0° and 90° azimuthal angles of FIG. 39. Therefore, byvarying 1 to increase the likelihood that the plane of incidence isparallel or perpendicular to the LC alignment direction, it can increaseuniformity of polarization conversion performance is accomplished acrossthe field-of-view.

For clarity in viewing, the thickness of the layer of liquid crystal,with stacks of liquid crystal molecules 4205 distributed along thethickness (e.g., parallel to the z axis) are not specificallyillustrated in FIG. 40. Instead, a front view of the spatial arrangementof the liquid crystal molecules 4205 as distributed across the lateraland/or radial spatial extent of the switchable waveplate 4202 (e.g.,first and second surfaces) is shown. As discussed above, in the exampleshown, the spatial arrangement corresponds to a plurality of rings 4203of liquid crystal molecules 4205. In various implementations, thisspatial arrangement is replicated through the thickness of the liquidcrystal layer. For example, the layer of liquid crystal may beconceptualized in certain implementations to be a stack of sheets ofliquid crystal wherein each sheet includes molecules 4205 having thesame spatial arrangement (e.g., concentric rings 4203 about the centralaxis) shown in FIG. 40. For a given lateral or radial position on thelayer, the orientation of the molecules 4205 (e.g., the angle ofrotation, φ) remains the same for different molecules located atdifferent distances (e.g., in the z direction) through the thickness ofthe layer from sheet to sheet. This leads to narrowband operationgenerally, where the improvement in polarization conversion efficiencyover the field-of-view applies to a narrow or limited range ofwavelengths centered around the center wavelength λc defined previously.Other configurations, however, are possible, for example as theconfiguration seen in FIG. 42A where the orientations of molecules arenot the same through the thickness of the layer, which can be used toincrease the bandwidth of this polarization conversion, e.g., providebroadband operation.

In various implementations, the first and second surfaces on theswitchable waveplate 4204 comprise surfaces on substrates. For example,the liquid crystal layer may be disposed between first and secondsubstrates. In various implementations, such as the design shown in FIG.40, the first and second surfaces comprise planar surfaces on planarsubstrates. The substrate may comprise glass or plastic material. Thesubstrate may comprise an optical element, such as quarter waveplates insome implementations.

As with other example switchable lens assemblies described herein, invarious implementations, the polarization switch or switchable waveplate4204 may further comprise a plurality of electrodes (not shown)configured to apply an electrical signal across the liquid crystallayer. This electrical signal may be used to switch the state of theliquid crystal and the polarization switch or switchable waveplate 4204.Accordingly, the polarization switch or switchable waveplate 4204 may beconfigured such that when the polarization switch is in one state, thepolarization of light incident thereon is rotated or otherwise convertedinto a different polarization state. For example, right handedcircularly polarized (RHCP) light incident on the polarization switch orswitchable waveplate 4204 may be rotated or converted into left handedcircular polarized (LHCP) light. However, when the polarization switch4104 is in another state, such conversion or rotation generally does notoccur.

FIG. 41 illustrates another example design for a switchable waveplate4304 configured to increase the efficiency of polarization rotation orconversion for light from objects on or near the periphery 4310 of thefield-of-view. The switchable waveplate 4304 includes a liquid crystallayer comprising molecules 4305 longer than wide along a longitudinaldirection 4332 thereof. The molecules 4305 are orientated such that thelongitudinal direction 4332 extends radially from a central axis 4324through the switchable waveplate 4304 for a plurality of radialdirections 4303 from the central axis. This configuration potentiallyincreases the uniformity in efficiency of polarization rotation orconversion of the switchable waveplate 4304 even for highly off-axisfield-of-view angles, in a similar fashion to the configuration seen inFIG. 40. While FIG. 40 is an example configuration where Φ is variedsuch that the plane of incidence is generally or substantially parallelto Φ across the field-of-view, in FIG. 41 the plane of incidence isgenerally or substantially perpendicular to Φ across the field-of-view.Both of the configurations illustrated in FIGS. 40 and 41 aim to achievethe relatively high polarization conversion performance of thesubstantially dark regions 3902 (e.g., corresponding to the 0° and 90°azimuthal angles) within FIG. 39 across the field-of-view.

The switchable waveplate 4304 includes a liquid crystal layer comprisingmolecules 4305 that are rotated in a different manner (e.g., in adifferent direction) than the switchable waveplate shown in FIG. 40. Theliquid crystal molecules 4305 in the switchable waveplate 4304illustrated in FIG. 41 are rotated about local axes 4301 parallel to acentral axis 4324 through the switchable waveplate. As shown, the localaxes 4301 go through the center of the liquid crystal molecule 4305 andare parallel to the central axis or optical axis 4324. Accordingly, invarious implementations, the longitudinal direction 4332 of themolecules 4305 are parallel to the first and second surface and thus therotation can be said to be in a plane parallel to the first and secondsurfaces. The amount of rotation of the molecule 4305, is represented byan angle, φ. This rotation depends on the location of the molecule 4305.Specifically, the orientations of the molecules 4305 (e.g., rotation bythe respective angles, φ, about local axes) can vary with azimuthalangle, Φ, about the central axis 4324 corresponding to the location ofthe molecule with respect to the central axis. In the illustratedimplementation, for example, the elongated molecules 4305 are generallyarranged in a plurality of radially extending directions 4303 about thecentral axis 4324.

FIG. 41, in particular, shows an example of an adaptive lens assembly4300 comprising a liquid crystal lens (e.g., waveplate lens) 4302 suchas a liquid crystal (LC) diffractive lens and the polarization switch(e.g., switchable waveplate) 4304, wherein the polarization switch orswitchable waveplate 4304 is flat or planar. The polarization switch orswitchable waveplate 4304 has first and second surfaces (e.g., outer andinner surfaces) and a liquid crystal layer disposed therebetween. Thefirst and second surfaces in this example are flat or planar. Asillustrated, the central axis is normal to the first and secondsurfaces. In contrast, light from objects 4308 on or near the periphery4310 of the field-of-view are shown incident on the switchable waveplate4304.

FIG. 41 illustrates the liquid crystal layer comprising a plurality ofliquid crystal molecules 4305 that are rotated about local axes 4301parallel to the central axis or optical axis 4324. These molecules 4305are rotated about the local axes 4301 by respective angles, φ, withrespect to a reference 4315 such as the horizon. The local axes 4301 areillustrated as parallel to the z-axis in FIG. 41. Likewise, the angularrotation, φ, is in a plane parallel to the x-y plane. Similarly, invarious implementations, the angular rotation, φ, is in a plane parallelto the first and second surfaces. This rotation can be referred to asazimuthal rotation about the respective (“local”) axis 4301 for themolecule 4305 (e.g., intersecting the center of the molecule) that isparallel to the central axis 4324.

The liquid crystal molecules 4305 are positioned at different locationsabout the central axis 4324. Accordingly, an azimuthal angle, Φ, may beused to specify the location, for example, in polar coordinates of theparticular molecule 4305 with respect to the central axis 4324. Invarious implementations of the switchable waveplate 4304, such as theimplementation shown in FIG. 41, the liquid crystal molecules 4305 arerotated about the local axes 4301 passing through the molecule by anangular (e.g., azimuthal) rotation, φ. This rotation is by an amountthat varies depending on the position of the molecule. In particular,the amount of rotation, φ, depends on the azimuthal angle, Φ,corresponding to the location, for example, in polar coordinates of theparticular molecule with respect to the central axis 4324. In variousimplementations, the liquid crystal molecules 4305 are generally longerthan wide along a longitudinal direction 4332. Additionally, theplurality of liquid crystal molecules 4305 are rotated about local axes4301 parallel to the central axis 4324 such that the longitudinaldirection 4332 of the molecule extends in a radial direction from thecentral axis. As a result, in various implementations, the molecules4305 have a particular spatial arrangement. In various implementations,for example, the molecules 4305 form radially directed lines disposedabout and extending from the central axis 4324 of the switchablewaveplate 4304. Accordingly, in some implementations, the molecules 4305may be arranged in these star-shaped or asterisk-shaped patterns. Theplurality of liquid crystal molecules 4305 can be rotated about thelocal axes 4301 parallel to the central axis 4324 such that longitudinaldirection 4332 of the respective molecule is parallel to a radialdirection from the central axis to the center of the molecule therebyforming this star or asterisk pattern. The longitudinal directions 4332of the molecules 4305 may be arranged along at least 3, 4, 5, 6, 8, 9,10, 12, 14, 20 or more (or any integer value in a range defined by anyof these values) linear paths that each intersect at a common point,such as the center. In various implementations, the arrangement of theliquid crystal molecules 4305 with the longitudinal direction 4332 formsa pattern that is symmetric with respect to an axis. This pattern my forexample have at least 3-fold, 4-fold, 5-fold, 6-fold, 7-fold, 8-fold,9-fold, 10-fold, 11-fold, 12-fold, 20-fold rotational symmetry withrespect to an axis (e.g., a central axis), or may have a degree ofsymmetry having an integer value in a range defined by any of thesevalues.

This spatial arrangement of the molecules 4305 may result in thepolarization conversion or rotation being more uniform across thepolarization switch 4304 as compared to a spatial arrangement where themolecules are oriented in the same direction for all locations (e.g.,all vertical or all horizontal). The polarization conversion or rotationof light incident along the central axis 4324 (e.g., optical axis)through the polarization switch 4304 (e.g., through the first and secondsurfaces and the liquid crystal layer) may, for example, be similar tothe polarization conversion or rotation for off-axis light coming fromobjects 4308 located at the periphery 4310 of the field-of-view. Thisresult may be a consequence of the rotated orientation of the individualliquid crystal molecules 4305, which increases the likelihood that theangle of incidence of light from different objects 4308 in thefield-of-view is substantially the same. In some implementations, forexample, the adaptive lens assembly 4300 is configured to transmit lightto a viewer's eye 4320 at a distance, d, from the adaptive lens assembly4300. Additionally, the longitudinal directions 4332 of the liquidcrystal molecules 4305 extends along respective projections of the path4334 of light from respective locations 4308 in a field-of-view of theviewer's eye 4320 to the viewer's eye that are projected onto the liquidcrystal layer. This arrangement aims to provide that the plane ofincidence is substantially perpendicular to Φ for a wide range of angles(e.g., always substantially perpendicular) of incidence, therebymimicking the 90° azimuthal angle performance shown in FIG. 39.

For clarity in viewing, the thickness of the layer of liquid crystal,with stacks of liquid molecules 4305 distributed along the thickness(e.g., parallel to the z-axis), are not specifically illustrated in FIG.41. Instead, a front view of the spatial arrangement of the liquidcrystal molecules 4305 as distributed across the lateral and/or radialspatial extent of the switchable waveplate 4302 (e.g., first and secondsurfaces) is shown. As discussed above, in the example shown, thespatial arrangement corresponds to a plurality of radially directedlines of liquid crystal molecules 4305. The spatial arrangement maycomprise, for example, a star-shaped or asterisk-shaped pattern. Invarious implementations, this spatial arrangement is replicated throughthe thickness of the liquid crystal layer. For example, the layer ofliquid crystal may be conceptualized in certain implementations to be astack of sheets or sublayers of liquid crystal wherein each sheetincludes molecules 4305 having the same spatial arrangement (e.g.,radially directed lines 4303 disposed about and extending from thecentral axis) shown in FIG. 41. For a given lateral or radial positionon the layer, the orientation of the molecules 4305 (e.g., the angle ofrotation, φ) remains the same for different molecules located atdifferent distances (e.g., in the z direction) through the thickness ofthe layer from sheet to sheet. As mentioned before, this may causenarrowband operation. Other configurations, however, are possible, forexample, for broadband operation, the location of molecules through thethickness of the layer may be changed.

In various implementations, the first and second surfaces on theswitchable waveplate 4304 comprise surfaces of substrates. For example,the liquid crystal layer may be disposed between first and secondsubstrates. In various implementations, such as the design shown in FIG.41, the first and second surfaces comprise planar surfaces of planarsubstrates. The substrate may comprise glass or plastic material. Thesubstrate may comprise an optical element, such as one or more quarterwaveplates, in some implementations.

As with other example switchable lens assemblies described herein, invarious implementations, the polarization switch or switchable waveplate4304 may further comprise a plurality of electrodes (not shown)configured to apply an electrical signal across the liquid crystallayer. This electrical signal may be used to switch the state of theliquid crystal and the polarization switch or switchable waveplate 4304.Accordingly, the polarization switch or switchable waveplate 4304 may beconfigured such that when the polarization switch is in one state, thepolarization of light incident thereon is rotated or otherwise convertedinto a different polarization state. For example, right-handedcircularly polarized (RHCP) light incident on the polarization switch orswitchable waveplate 4304 may be rotated or converted into left handedcircular polarized (LHCP) light or vice versa. However, when thepolarization switch 4304 is in another state, such conversion orrotation generally does not occur.

The performance of polarization switches/switchable waveplates can bequantified as a leakage. For example, for converting the handedness ofcircular polarization, the leakage may be defined as the percent (%) oflight leaking through a pair of parallel circular polarizers(right/left) with the polarization switch/switchable waveplate inbetween, with 100% baseline calculated or measured from the polarizersbut without the switch in between. Further, this leakage can be averagedover the target field-of-view (e.g., ±35° cone angle) and the wavelengthrange of operation (e.g., 420 nm to 680 nm to cover most of the visiblerange). This polarization leakage can also be measured using a tool suchas an ellipsometer to compare with theoretical predictions. As anexample, the polarization leakage measured from an off-the-shelf ECBcell, with properties similar to those shown in FIG. 39, can be about10% averaged over ±35° incident cone angle and across 420 nm to 680 nm,which can result in substantial visual artifacts in some applications.With the approaches in FIGS. 40, 41, and 42, this leakage value can beimproved from 10% to <5% or <2%, which is a substantial improvement.Thus the leakage may be less than or equal to 5%, 4%, 3%, 2% 1% or havea value in any range defined by any of these values. Alternatively toquantifying the performance as leakage percent, the performance can becharacterized instead in terms of diffraction efficiency percent.

In some designs, such as for example, those described in FIGS. 40 and41, the plurality of liquid crystal molecules having said rotationvarying with azimuthal angle about said central axis include at least50%, 60%, 70%, 80% 90%, 95% or more (or a percentage in any rangedefined by any of these values) of the molecules extending over a rangeof at least 1, 2, 3, 4, 5, 6, 8, 10, 12 cm² or more (or any rangedefined by any of these values) across the liquid crystal layer and/orwaveplate. Similarly, the plurality of liquid crystals molecules may bearranged in concentric rings having a size of at least 1, 2, 3, 4, 5, 6,8, 10, 12 cm² or more (or a size in any range defined by any of thesevalues). In other examples, the plurality of liquid crystals moleculesmay be arranged in the shape of an asterisk or star having a size of atleast at least 1, 2, 3, 4, 5, 6, 8, 10, 12 cm² or more (or a sized inany range defined by any of these values). In various implementations,the arrangement of liquid crystal molecules with the longitudinaldirection 4332 forms a pattern that is symmetric with respect to anaxis. This pattern may, for example, have at least 3-fold, 4-fold,5-fold, 6-fold, 7-fold, 8-fold, 9-fold, 10-fold, 11-fold, 12-fold, or20-fold rotational symmetry with respect to an axis (e.g., a centralaxis) or have a degree of symmetry having an integer value in a rangedefined by any of these values.

As discussed above in connection with FIGS. 13C, 20A, and 20B, highbandwidth capability (e.g., uniformity in performance across multiple orbroad range of wavelengths) of a waveplate can be achieved byparticularly configuring the twist arrangement of liquid crystalmolecules vertically within one or more liquid crystal layers asillustrated in FIG. 42A. Such a configuration may, for example, increasethe diffraction efficiency, which in turn, increases the amount of lightthat undergoes polarization rotation or conversion.

FIG. 42A schematically illustrates a cross-sectional view of a broadbandswitchable waveplate 4404 comprising a plurality of liquid crystallayers 4418A, 4418B. The illustrated broadband waveplate lens 4404comprises two liquid crystal layers 4418A, 4418B having liquid crystalmolecules 4405 that have opposite twist sense. The thickness and twistangles of the two layers 4418A, 4418B provide additional degrees offreedom to increase, improve, or optimize the polarization conversionover a wider range of wavelengths, as compared to just control and/or asingle liquid crystal layer. Accordingly, the layers 4118A, 4118B canhave thicknesses (possibly that are different) that provide for (andpossibly increase) the polarization conversion efficiency over a widerrange of wavelengths. FIG. 42A depicts a cross-sectional view of theliquid crystal layers 4418A, 4418B.

The liquid crystal layers 4418A, 4418B are shown included in two cells4450A, 4450B labeled Cell 1 and Cell 2. In the implementationschematically illustrated in FIG. 42A, the first liquid crystal layer4418A associated with the first cell 4450A (Cell 1) is disposed betweena pair of substrates 4452A, 4452B and a pair of electrodes 4454A, 4454B.The second liquid crystal layer 4418B associated with the second cell4450B (Cell 2) is disposed between a pair of substrates 4456A, 4456B anda pair of electrodes 4458A, 4458B. An interface 4460 separates the twocell 4450A, 4450B and hence the two liquid crystal layers 4418A, 4418B.Alignment layers (not shown) may be included adjacent the liquid crystallayers 4418A, 4418B in the two cells 4450A, 4450B to align assist in theorientation of the liquid crystal molecules 4405. For example, in thefirst cell 4450A, an alignment layer may be disposed adjacent the firstliquid crystal layer 4418A proximal to the first substrate 4452A and/orfirst electrode 4454A. Similarly, in the second cell 4450B, an alignmentlayer may be disposed adjacent the second liquid crystal layer 4418Bproximal to the first substrate 4156A and/or first electrode 4458A.Spacer beads or structures (not shown) may be added in between thealignment layers to increase or improve the uniformity of the thicknessof the liquid crystal layer over the active area of the device. Otherarrangements of the substrates, electrodes, and/or alignment layers arepossible.

One example of the twisting arrangement of the liquid crystal molecules4405 is schematically illustrated in the cross-section shown in FIG.42A. The thickness of both the liquid crystal layers 4418A and 4418B canbe chosen to be around half-wave thickness defined previously. Theliquid crystal molecules 4405 in the first and second liquid crystallayers 4418A, 4418B have opposite twist sense, e.g., opposite twistangles. For example, liquid crystal molecules 4405 in the second liquidcrystal layer 4418B can be twisted with distance (e.g., along the zdirection) from the first liquid crystal layer 4418A so as to mirror thetwist of the molecules in the first liquid crystal layer. The liquidcrystal molecules 4405 of the first and second liquid crystal layers4418A, 4418B can be, for example, symmetrically twisted with respect tothe interface 4460 between the first and second layers. This twist mayhave a net angle between about 60 degrees and 80 degrees. For example,the twist angles may be 70° and −70° respectively for the first andsecond liquid crystal layers 4418A, 4418B in the first and second cells4450A, 4450B. The twist may be introduced in some implementations bydoping the liquid crystal material with a chiral agent, and/or adjustingthe orientation angle of the alignment layers adjacent to the liquidcrystal layers.

The lateral arrangement of the liquid crystal molecules 4405 across aplane parallel to the x-y plane at a given depth in the z direction,however, can vary depending on the design of the switchable waveplate4404 and can, for example, have any of the various arrangementsdescribed above, including the spatial arrangement illustrated abovewith respect to FIG. 40, as well as others. For example, in someimplementations, the liquid crystal molecules 4405 closest to a firstsubstrate 4452A can generally have local orientation directions, e.g.,local elongation directions or local directors that vary as a functionof the position of the molecule (e.g., as specified by the azimuthalangle, Φ, with respect to the central region or axis) in a similarmanner as described above with respect to FIG. 40. In someimplementations, for example, the liquid crystal molecules 4405 arelonger than wide along a longitudinal direction and can have elongatedsides along the longitudinal direction that face the central region oraxis so as to form a plurality of ring-shaped arrangements of liquidcrystal molecules such as illustrated in FIG. 40. Other lateralarrangement and local orientation of the liquid crystals are possible.

In addition, the arrangement of liquid crystal molecules 4405 in a givencolumnar region in the two liquid crystal layers 4418A, 4418B (see FIG.42A) can be expressed as having the nematic director n which varies as afunction of vertical location (depth along the z direction) within theliquid crystal layer 4418A, 4418B. As discussed above, in variousdesigns, a given column of liquid crystal molecules 4405 will twist withdepth through the respective liquid crystal layers 4418A, 4418B. Inaddition, in various designs such as illustrated in FIG. 42A, for agiven column of liquid crystal molecules 4405 having a first sense oftwist in one of the liquid crystal layers 4418A, 4418B, a correspondingcolumn of liquid crystal molecules in the other of the liquid crystallayers 4418A, 4418B has an opposite sense of twist. In other words, asdiscussed above, liquid crystal molecules 4405 in the two liquid crystallayers 4418A, 4418B have arrangements that may form mirror images ofeach of other about the interface 4160 between the two liquid crystallayers 4418A, 4418B. In some implementation, such a configuration of thefirst and second liquid crystal layers 4418A, 4418B can provide forincreased uniformity in altering the polarization state of lightincident thereon across multiple wavelengths in comparison toconfigurations having one of the first liquid crystal layer 4418A or thesecond liquid crystal layer 4418B alone. Such a configuration may insome cases increase the diffraction efficiency of the switchablewaveplate across a range of wavelengths. The switchable waveplate may,for example, be configured to diffract light at a diffraction efficiencygreater than 90% or greater than 95% possibly 96%, 97%, 98%, 99%, 99.5%,99.9%, or 100% (or a percentage within any range defined by any of thesevalues) within a wavelength range including at least 450 nm to 630 nm.

In some designs, reactive mesogens can be employed to create thearrangement of liquid crystal molecules 4405 in the two liquid crystallayers 4418A, 4418B. In some implementations, reactive mesogens havinglow molecular weight can be used such that the molecules 4405 may bealigned by surfaces and have a twist to create complex profiles.

For example, by suitably configuring the alignment layer farthest fromthe second liquid crystal layer 4418B, e.g., proximal the firstsubstrate 4452A and/or first electrode 4454A, the liquid crystalmolecules closest to this alignment layer (e.g., leftmost in FIG. 42A)can be arranged to have a first plurality of local azimuth angles (ϕ) ofelongation directions of the liquid crystal molecules 4405. These localazimuth angles, ϕ, about local axes parallel to the central axis canhave, for example, an arrangement as described above with respect toFIG. 40. In addition, the liquid crystal molecules 4405 adjacent these(e.g. leftmost) liquid crystal molecules in the first liquid crystallayer 4418A can be configured to have a first twist by adding chiralagents to the first liquid crystal layer 4418A, such that the liquidcrystal molecules (e.g., rightmost in FIG. 42A), for example, closest tothe second liquid crystal layer 4418B, have second plurality of azimuthangles, ϕ. Thereafter, by suitably configuring the alignment layer,e.g., proximal the first substrate 4456A, in the second cell 4450B,liquid crystal molecules 4405 in the second liquid crystal layer 4418Bclosest to the first liquid crystal layer 4418A can be arranged to havethe third plurality of local azimuth angles, ϕ, of elongation directionsof the liquid crystal molecules 4405. In addition, the adjacent liquidcrystal molecules 4405 in the second liquid crystal layer 4418B can beconfigured to have a second chiral twist by adding chiral agents to thesecond liquid crystal layer 4418B, such that the liquid crystalmolecules farthest from the first liquid crystal layer 4418A (e.g.,rightmost in FIG. 42A), for example, closest to the second substrate4456B and/or second electrode 4458B in the second cell 4450B, have afourth plurality of local azimuth angles, ϕ. In some embodiments, thefirst and second chiral twist is about the same, such that the liquidcrystal molecules 4405 of the first liquid crystal layer 4418A farthestfrom the second liquid crystal layer 4418B (e.g., leftmost in FIG. 42A),for example, closest to the first substrate 4452A and/or electrodes4454A, and the liquid crystal molecules 4405 of the second liquidcrystal layer 4418B farthest from the first liquid crystal layer 4418A(e.g., rightmost in FIG. 42A), for example, closest to the secondsubstrate 4456B and/or the second electrodes 4458B in the second cell4450B, have the same azimuth angles.

Accordingly, FIG. 42A shows the first liquid crystal layer 4418Acomprising a plurality of sublayers 4466A, 4466B, 4466C, 4466Dcomprising liquid crystal molecules 4405. The sublayers 4466A, 4466B,4466C, 4466D include a first sublayer 4466A in the first liquid crystallayer 4418A farthest from the second liquid crystal layer 4418B. Thesublayers 4466A, 4466B, 4466C, 4466D in the first liquid crystal layer4418A include additional sublayers 4466B, 4466C, 4466D having liquidcrystal molecules 4405 that may generally have the same positions in thex-y plane (e.g., laterally or radially) as the liquid crystal molecules4405 included in the first sublayer 4466A and progressively twistedabout local axes parallel to a central axis. The amount of twistincreases with distance from the first sublayer 4466A.

The second liquid crystal layer 4418B can also comprises a plurality ofsublayers 4468A, 4468B, 4468C, 4468D. This plurality of sublayers 4468A,4468B, 4468C, 4468D have liquid crystal molecules 4405 that maygenerally have the same positions in the x-y plane (e.g., laterally orradially) as the liquid crystal molecules included in the first sublayer4468A of the second liquid crystal layer 4418B. The liquid crystalmolecules 4405 in the plurality of sublayers 4468B, 4468C, 4468D in thesecond liquid crystal layer 4418B are progressively twisted about localaxes parallel to the central axis, the amount of twist increasing withdistance from the first sublayer 4468A in the second liquid crystallayer 4418B.

As illustrated, the liquid crystal sublayer 4468A in the second liquidcrystal layer 4418B closest to the first liquid crystal layer 4418A canhave liquid crystal molecules 4405 with the same orientation as theplurality of liquid crystal molecules 4405 in the sublayer 4466D in thefirst liquid crystal layer 4418A that are closest to the second liquidcrystal layer 4418B.

Also as illustrated, the second liquid crystal layer 4418B can have aliquid crystal sublayer 4468D farthest from to the first liquid crystallayer 4418A having liquid crystal molecules 4405 with the sameorientation as the plurality of liquid crystal molecules 4405 in thefirst sublayer 4466A in the first liquid crystal layer 4418A.

Accordingly, the liquid crystal molecules 4405 in the first and secondliquid crystal layer 4418A, 4418B can be oppositely twisted. Suchopposite twists may provide more broadband performance, for example,increasing the diffraction efficiency and/or polarization rotationand/or conversion efficiency across multiple wavelengths.

In one example configuration, the liquid crystal layers 4418A, 4418Bhave suitable thickness, e.g., between about 1 μm and 2 μm or betweenabout 1.5 μm and 2 μm, for instance about 1.7 μm. A suitable chiraltwist may be, but not limited to, between about 50 degrees and 90degrees or between about 60 degrees and 80 degrees, for instance about70 degrees or any range between any of these values. The relativebandwidth Δλ/λ_(o) may be, but are not limited to, greater than 40%, 50%or 60%, for instance about 56%, or a percentage in any range between anyof these values. Within the operating wavelength range such as thewavelength range above, the diffraction efficiency may be greater thanany of 90%, 95%, 97%, 98%, 99%, or 99.5%, or a percentage in any rangebetween any of these values, according to certain implementations. Anycombination of these ranges and values are possible. Additionally, othervalues may also be possible.

As described herein, the liquid crystal device may be switchable. Theswitchable waveplate, for example, can have multiple states wherein theliquid crystal molecules 4405 are caused to change orientation byapplying an electrical signal to the liquid crystal layers 4418A and/or4418B. As illustrated in FIG. 42B, for example, first and secondelectrical sources 4470A, 4470B apply electrical signals (e.g.,voltages) to the first and second liquid crystal layers 4418A, 4418B,respectively. The first electrical source 4470A is shown, for example,to be electrically connected to the first and second electrodes 4454A,4454B disposed about the first liquid crystal layer 4418A. Similarly,the second electrical source 4470B is shown, for example, to beelectrically connected to the first and second electrodes 4458A, 4458Bdisposed about the second liquid crystal layer 4418B. Accordingly, FIG.42B shows the liquid crystal molecules 4405 in the first and secondlayers 4418A, 4418B as oriented differently as a result of applicationof an electrical signal in comparison to the orientation of the liquidcrystal molecules shown in FIG. 42A where no electrical signal is shownapplied to the liquid crystal layers. Other configurations are possible.For example, the arrangement and/or placement of the electrodes may bedifferent. Similarly, although zero voltage or electrical signal isdepicted as being applied to the liquid crystal layers 4418A, 4418B inFIG. 42A, other voltages or signals may be applied.

A wide range of nematic liquid crystal molecules can be used toconstruct the various embodiments described herein. Additionally, chiraldopant agents could be added to the liquid crystals to control the twistangles. Vendors such as Merck Ltd., DIC Corporation Ltd. are suppliersfor such materials. Additionally, passive waveplates that convertpolarization between the switches and other elements could be used aswell. These waveplates or retarders, for example, could be quarter-waveplates that convert between linear and circular polarization states.These or retarders could be formed, for example, from liquid crystalmaterials, birefringent minerals (calcite, quartz, etc.), stretchedpolymers (polycarbonate, etc.) or other ways or combinations of any ofthese.

Various methods may be employed to fabricate such liquid crystal opticalelements including methods disclosed in U.S. Patent App. Pub. Nos.2018/0143470 and 2018/0143485, both of which are incorporated herein byreference in their entirety.

Fabrication of Optical Elements Comprising Tilted Liquid CrystalMolecules

Various methods may be used to orient liquid crystal molecules andprovide a desired amount of tilt with respect to the substrates. Thetechniques described herein may be useful for fabricating opticalelements and may be beneficial for other optical technologies utilizingliquid crystal devices. Example applications include liquid crystaldisplays (both transmissive and liquid crystal on silicon (LCoS)),adjustable light shutters/dimmers, etc. Some of such example methods areprovided below.

In certain designs, one or more vertical alignment layers and horizontalalignment layers are used in combination to orient liquid crystalmolecules and provide the desired oblique tilt angle or pre-tilt. Forinducing vertical alignment of liquid crystals, certain polyimidematerials are coated as thin films using standard techniques (spincoating slot coating, etc.), baked, and then mechanically rubbed tocreate a preferential azimuthal direction of tilt when an externalvoltage is applied. Other materials and methods may also be used.

FIG. 43A illustrates a cross-sectional view of a device 4500A comprisinga pair of substrates 4501A, 4502A and a pair of respective verticalalignment layers 4503A, 4504A. A layer of LC molecules 4505A is disposedbetween the two alignment layers 4503A, 4504A. The vertical alignmentlayers 4503A, 4504A in the device 4500A shown in FIG. 43A creates ahomeotropic alignment of LC molecules 4506A. As illustrated, the liquidcrystal (LC) molecules 4506A in the layer of liquid crystals 4505A havelengths longer than widths and are oriented with their lengths directedin a direction crossing, e.g., orthogonal to, the main surfaces of thepair of substrates 4501A, 4502A and the pair of respective verticalalignment layers 4503A, 4504A. In this example, the lengths are orientedparallel to the z-axis, which is perpendicular to the pair of substrates4501A, 4502A and the pair of respective vertical alignment layers 4503A,4504A. The long axes of the LC molecules 4506A are be oriented aboutnormal or about 90° with respect to the substrates 4501A, 4502A and thevertical alignment layers 4503A, 4504A. Likewise, FIG. 43A shows LCmolecule 4506A with orientation angle θ of about 90° with respect to thesubstrates 4501A, 4502A and the vertical alignment layers 4503A, 4504A.This direction is referred to as the vertical direction. The verticalalignment layers 4503A, 4504A are configured to cause said liquidcrystal (LC) molecules 4506A to be oriented such that said lengths aredirected more along in this vertical direction (and orthogonal to thehorizontal direction).

FIGS. 43B and 43C illustrate perspective views of a device 4500B/4500Csimilar to FIG. 43A. FIG. 43B/FIG. 43C illustrates the device4500B/4500C comprising a pair of substrates 4501B/4501C, 4502B/4502C anda pair of respective vertical alignment layers 4503B/4503C, 4504B/4504C.In addition, the device 4500B/4500C of FIGS. 43B-43C further comprises apair of horizontal alignment layers 4507B/4507C, 4508B/4508C. A liquidcrystal layer 4505B/4505C comprising liquid crystal molecules4506B/4506C is disposed between the pair of substrates 4501B/4501C,4502B/4502C. Similarly, the liquid crystal layer 4505B/4505C is disposedbetween the pair of vertical alignment layers 4503B/4503C, 4504B/4504C.The liquid crystal layer 4505B/4505C is also disposed between the pairof horizontal alignment layers 4507B/4507C, 4508B/4508C. In FIG. 43B,the horizontal alignment layers are parallel to each other to maintainuniform alignment throughout the liquid crystal layer, while in FIG.43C, the horizontal alignment layers are perpendicular to each other inorder to induce a twist in the liquid crystal layer. As discussed above,the liquid crystal (LC) molecules 4506B/4506C in the layer of liquidcrystal 4505B/4505C have lengths longer than widths. Additionally, asdiscussed above with respect to FIG. 43A, the vertical alignment layers4503B/4503C, 4504B/4504C are configured such that the liquid crystal(LC) molecules 4506B/4506C are oriented with the lengths of the LCmolecules directed more along the vertical direction (e.g. z direction)than the horizontal direction (e.g., x direction). In contrast, thehorizontal alignment layers 4507B/4707C, 4508B/4508C are configured suchthat liquid crystal (LC) molecules 4506B/4506C are oriented with thelengths of the LC molecules directed more along said horizontaldirection than the vertical direction. In various implementations, thevertical alignment layer(s) 4503B/4503C, 4504B/4504C causes liquidcrystal molecules 4506B/4506C to be oriented more vertical than withoutthe vertical alignment layer(s) and the horizontal alignment layer(s).In various implementations, the horizontal alignment layers 4507B/4507C,4508B/4508C cause liquid crystal molecules 4506B/4506C to be morehorizontal than without the vertical alignment layer(s). In variousimplementations, the vertical alignment layer(s) 4503B/4504C,4504B/4504C is/are configured to cause liquid crystal (LC) molecules4506B/4506C proximal thereto to be oriented more along the verticaldirection than said horizontal direction. Similarly, in variousimplementations, the second horizontal alignment layer(s) 4507B/4507C,4508B/4508C is/are configured to cause liquid crystal (LC) molecules4506B/4506C proximal thereto to be more along the horizontal directionthan the vertical direction.

Still referring to FIGS. 43B and 43C, the vertical and horizontalalignment layers 4503B/4503C, 4504B/4504C, 4507B/4507C, 4508B/4508C areparallel to the substrates 4501B/4501C, 4502B/4502C. Accordingly, anormal to the vertical and horizontal alignment layers 4503B/4503C,4504B/4504C, 4507B/4507C, 4508B/4508C is parallel to the normal throughthe substrates 4501B/4501C, 4502B/4502C. Likewise, in variousimplementations, the vertical alignment layer(s) 4503B/4503C,4504B/4504C are configured to cause the liquid crystal (LC) molecules4506B/4506C to be oriented such that the lengths are directed more alonga vertical direction orthogonal to the substrates 4501B/4501C,4502B/4502/C, the vertical alignment layer(s) 4503B/4503C, 4504B/4504C,and/or the horizontal alignment layer(s) 4507B/4507C, 4508B/4508C than ahorizontal direction parallel to the substrate and the vertical alimentlayer(s) and/or the horizontal alignment layer(s).

In various implementations, the contributions of the vertical andhorizontal alignment layers 4503B/4503C, 4504B/4504C, 4507B/4507C,4508B/4508C is to cause the liquid crystal molecules 4506B/4506C to betilted with respect to the horizontal and vertical directions. Theliquid crystal layer 4505B/4505C is disposed with respect to verticaland horizontal alignment layers 4503B/4503C, 4504B/4504C, 4507B/4507C,4508B/4508C such that the orientations of liquid crystal molecules4506B/4506C are influenced by both the vertical and horizontal alignmentlayers 4503B/4503C, 4504B/4504C, 4507B/4507C, 4508B/4508C and areoriented at an oblique angle with respect to the vertical and horizontaldirections. The liquid crystal molecules 4506B/4506C thus have a pretilt angle.

The pretilt angle or oblique angle of the longitudinal directions of theLC molecules 4506B/4506C can be controlled to be between 0° and 90° withrespect to the normal to the substrate 4501B/4501C, 4502B/4502C,vertical alignment layer(s) 4503B/4503C, 4504B/4504C and/or horizontalalignment layer(s) 4507B/4507C, 4508B/4508C and with respect to thez-axis orthogonal to the x-y plane shown in FIGS. 43B-43C. The amount ofpre-tilt or the oblique angle may depend on the relative alignmentstrengths of the contributions of the vertical and horizontal alignmentlayers 4503B/4504C, 4504B, 4507B, 4508B to the LC molecules'orientation. In some implementations, the pretilt angle or oblique anglefor most of the LC molecules 4506B can be between 5° and 85°. In someimplementations, the pretilt angle or oblique angle can be between 45°and 90°, for example, between 50° and 85° for most of the LC molecules4506B/4506C. In some implementations, the pretilt angle or oblique anglecan be between 0° to 45°, for example between 5° and 40° for most of theLC molecules 4506B/4506C. Any value in a range defined by any of thesevalues is possible. In some implementations, at least a portion of theLC molecules 4506B/4506C are at 0° and/or 90°. In various designs, mostLC molecules 4506B/4506C can have a pre-tilt angle or be orientedoblique with respect to the vertical and horizontal direction (e.g.,have an orientation other than 90° or other than 90° or 0°).

As illustrated in FIGS. 43B and 43C, the one or more horizontalalignment layers 4507B/4507C, 4508B/4508C may have a topographicalrelief configured to influence the orientation of liquid crystalmolecules 4506B proximal thereto. The one or more horizontal alignmentlayers 4507B/4507C, 4508B/4508C may, for example, comprise features suchas surface relief features (e.g., elongate features such as lines)configured to influence the orientation of liquid crystal molecules4506B/4506C proximal thereto.

Accordingly, the one or more horizontal alignment layers 4507B/4507C,4508B/4508C may comprise a patterned layer. The one or more horizontalalignment layers 4507B/4507C, 4508B/4508C may comprise an imprint layerwhich may, for example, be formed by imprinting, e.g., using an imprinttemplate. In some implementations, the one or more horizontal alignmentlayers 4507B/4507C, 4508B/4508C may comprise a nanoimprint layer, forexample, be formed by nano-imprinting, e.g., with a nano-imprinttemplate.

Example processes of imprinting the topographically varying horizontalalignment layer 4507B/4507C, 4508B/4508C were described for forming theimprinted alignment layer 3004 with respect to FIG. 30A. However, theprocesses of forming topographically varying horizontal alignment layers4507B/4507C, 4508B/4508C of FIGS. 43B-43C may be performed overrespective vertical alignment layers 4503B/4503C, 4504B/4504C in someimplementations.

While an example imprinting process (e.g. a nanoimprinting process) forforming topographically varying horizontal alignment layers wasdescribed for forming the topographically varying horizontal alignmentlayers 4507B/4507C, 4508B/4508C with respect to FIGS. 43B-43C, otherembodiments are not so limited. In other embodiments, the horizontalalignment layers 4507B/4507C, 4508B/4508C can be fabricated using otherpatterning techniques including lithography and etch.

In addition, while the topographically varying alignment layers4507B/4507C, 4508B/4508C were described as being formed of a polymericmaterial, designs are not so limited and in various other embodiments,the horizontal alignment layers 4507B/4507C, 4508B/4508C can comprise adielectric material, e.g., silicon or a glass material.

Still referring to FIGS. 43B and 43C, as discussed above, thetopographically varying horizontal alignment layer(s) 4507B/4507C,4508B/4508C may have a varying topographic surface (e.g., features suchas elongate features) configured to influence the orientation of liquidcrystal molecules 4506B/4506C. Characteristics of the features mayaffect the amount that these features influence the orientation ofliquid crystal molecules 4506B/4506C proximal thereto. In some designs,for example, the alignment strength of the topographically varyinghorizontal alignment layer 4507B/4507C, 4508B/4508C is controlled by theheight, width, pitch, duty cycle (linewidth vs. spacing), profiles(round vs. square profiles) or aspect ratios or any combinations thereofof the varying topographic surface and features (e.g., topographical orsurface features). The features may comprise, for example, topographicalfeatures or surface relief features having a size (e.g., height, width,length or any combinations thereof) that may be varied, for example,increased or decreased to increase or decrease the effect of thehorizontal alignment layers 4507B/4507C, 4508B/4508C on the orientationof liquid crystal molecules 4506B/4506C at least in the proximity ofthese features. The features may comprise, for example, a plurality offeatures or surface relief features spaced apart (either with regularspacing and periodicity or irregular spacing/periodicity or combinationsthereof) and may have a pitch, periodicity, spacing or any combinationthereof that may be varied, for example, increased or decreased toincrease or decrease the effect (e.g., strength of the effect) of thehorizontal alignment layers 4507B/4507C, 4508B/4508C on the orientationof liquid crystal molecules 4506B/4506C at least in the proximity ofthese features. The features may comprise, for example, a plurality offeatures or surface relief features with shapes or profiles such ascross-sectional profiles (e.g., rounded versus square, rectangle,triangle, or other or combinations thereof), aspect ratios (e.g., heightversus width or height versus length or length versus width orcombinations thereof) or any combination thereof that may be varied, forexample, increased or decreased, to increase or decrease the effect(e.g., strength of the effect) of the horizontal alignment layers4507B/4507C, 4508B/4508C on the orientation of liquid crystal molecules4506B/4506C at least in the proximity of these features. The featuresmay comprise, for example, a plurality of features or surface relieffeatures with shapes or profiles such as cross-sectional profiles withduty cycles (e.g., ratio of area corresponding to high portions to areacorresponding to low portions of a surface having topographicallyvariation such as height variation) that may be varied, for example,increased or decreased, to increase or decrease the effect (e.g.,strength of the effect) of the horizontal alignment layers 4507B/4507C,4508B/4508C on the orientation of liquid crystal molecules 4506B atleast in the proximity of these features. Other variations in thefeatures, surface topography, or other characteristics of the horizontalalignment layers 4507B/4507C, 4508B/4508C may be varied and/orcontrolled to influence, increase, or decrease the effect (e.g.,strength of the effect) of the horizontal alignment layers 4507B/4507C,4508B/4508C on the orientation of liquid crystal molecules 4506B/4506C.

As discussed below (see FIG. 43D), the horizontal alignment layer(s)4507B/4507C, 4508B/4508C can have different regions that influence theorientation of liquid crystal molecule 4506B/4506C proximal thereto bydifferent amounts. Accordingly, the orientation (e.g. pre-tilt) of theLC molecules 4506B/4506C can vary across the liquid crystal layer4505B/4505C. For example, a first region may be configured to cause theliquid crystal molecules 4506B/4506C proximal thereto to be morehorizontal than liquid crystal molecules 4506B/4506C more proximal to asecond region. In this manner, the orientation (e.g., pre-tilt) of theliquid crystal molecules 4506B/4506C may be varied across the opticalelement.

In some implementations, the vertical alignment strength is controlledand/or affected by the thickness of the vertical alignment layer.Thicker vertical alignment layers 4503B/4503C, 4504B/4504C may, forexample, possibly more strongly influence LC molecules 4506B/4506C tohave a vertical orientation (e.g., have a length greater than width thatis aligned more parallel to the vertical direction). For example, if athicker vertical alignment layer 4503B/4503C, 4504B/4504C as opposed toa thinner vertical alignment layer is used in combination with ahorizontal alignment layer 4507B/4507C, 4508B/4508C, the pre-tilt anglemay be more parallel to the vertical direction with the thickeralignment layer as compared to the thinner vertical alignment layer4503B/4503C, 4504B/4504C used in combination with the same horizontalalignment layer 4507B/4507C, 4508B/4508C.

Similarly, the vertical alignment layer(s) 4503B/4503C, 4504B/4504C canhave different regions that influence the orientation of liquid crystalmolecules 4506B/4506C proximal thereto by different amounts. Forexample, a first region may be configured to cause the liquid crystalmolecules 4506B/4506C proximal thereto to be more vertical than liquidcrystal molecules 4506B/4506C more proximal to a second region. Thethickness of the vertical alignment layers 4503B/4503C, 4504B/4504C may,for example, be varied (e.g., increased or decreased) in differentregions across the vertical alignment layers 4503B/4503C, 4504B/4504C toincrease or decrease the effect (e.g., strength of the effect) of thevertical alignment layer on the orientation of liquid crystal molecules4506B/4506C at least in the proximity of the respective region.Accordingly, the orientation (e.g. pre-tilt) of the LC molecules4506B/4506C can vary across the liquid crystal layer 4505B/4505C. Inthis manner, the orientation (e.g., pre-tilt) of the liquid crystals4506B/4506C may be varied across the optical element.

In some implementation, the horizontal alignment layer(s) 4507B/4507C,4508B/4508C may comprise regions configured not to cause said obliqueangle to be more horizontal. Accordingly, the horizontal alignmentlayers 4507B/4507C, 4508B/4508C may comprise at least one regionconfigured not to cause pretilt between two regions of the horizontalalignment layers 4507B/4507C, 4508B/4508C configured to introduce anoblique angle or cause pretilt.

Similarly, in some implementations, in some implementation, the verticalalignment layer(s) 4503B/4503C, 4504B/4508C may comprise regionsconfigured not to cause to be more vertical. Accordingly, the verticalalignment layer(s) 4503B/4503C, 4504B/4504C may comprise at least oneregion configured not to cause the LC molecules 4506B/4506C to bevertical disposed between two regions of the vertical alignment layer(s)4503B/4503C, 4504B/4504C configured to cause the LC molecules to be morevertical.

FIG. 43D illustrates an example of a horizontal alignment layer havingdifferent regions that influence the orientation of liquid crystalmolecule proximal thereto by different amounts. In particular, FIG. 43Dshows a portion of a device 4500D comprising a substrate 4502D, avertical alignment layer 4504D, and a horizontal alignment layer. Thehorizontal alignment layer comprises topographically varying surfacefeatures 4508D, 4510D that influence the orientation of liquid crystalmolecules 4518D, 4522D proximal thereto. The horizontal alignment layerincludes a plurality of regions in areas 4512D, 4516D of the devicehaving topographical surface features (e.g., nanofeatures) 4508D, 4510Darranged in patterns (e.g., nanostructure patterns) configured toinfluence the orientation of LC molecules 4518D, 4522D proximal thereto.The horizontal alignment layer also includes a region in an area 4514Dof the device without such topographical surface features (e.g.,nanofeatures) configured to influence the orientation of LC molecules4520D proximal thereto. This area 4514D where the horizontal alignmentlayer does not include such topographical surface features (e.g.,nanofeatures) configured to influence the orientation of LC molecules4520D proximal thereto is disposed between the two areas 4512D, 4516Dwhere the horizontal alignment layer has topographical surface features4508D, 4510D that are configured to influence the orientation of LCmolecules 4518D, 4522D proximal thereto.

The different regions corresponding to the different areas 4512D, 4514D,4516D of the device have different amounts of strength to influence theorientation of the alignment of the LC molecule 4518D, 4522D, 4520D inthose areas. Accordingly, the LC molecules 4518D, 4520D, 4522D in thedifferent areas 4512D, 4514D, 4516D have different amounts of pretiltand different orientation angles (θ₁, θ₂, θ₃). The LC molecules in thearea 4514D where the horizontal alignment layer is without patternednanostructures are primarily influenced by the vertical alignment layer.As a result the orientation angles of the molecules (of the length ofthe molecule with respect to the horizontal direction) are about 90°. InFIG. 43D, the LC molecules 4520D in this region 4514D are shown havingangle θ₂ of about 90°.

In contrast, the vertical alignment layer in the surrounding areas4512D, 4516D is configured to cause the LC molecules 4518D, 4522D inthese areas to have a pretilts and oblique angles θ₁, θ₃. Moreover, thetopographical features 4508D, 4510D have different characteristics,namely different sizes, such that the vertical alignment layer in thesurrounding areas 4512D, 4516D influence the orientation of the LCmolecules 4518D, 4522D in these areas by different amounts. Inparticular, the elongate topographic features 4510D in the area 4516Dhave a greater height and width than the elongate topographic features4508D in the area 4512D. Likewise, the elongate topographic features4510D in the area 4516D have greater influence on the orientation of therespective LC molecules 4518D, 4522D than the elongate topographicfeatures 4508D in the area 4512D. The LC molecules 4522D in the area4516D are therefore more horizontal than the LC molecules 4518D in thearea 4512D. In the illustrated example, shown in FIG. 43D, for example,θ₁>θ₃. The LC molecules 4518D in the area 4512D are more vertical thanLC molecules 4522D in the area 4516D.

Although example configurations are shown in FIGS. 43A-43D, a wide rangeof other configuration and variations, however, are possible. Forexample, the features in the horizontal alignment layer may vary moreprogressively, for example, to create a progressive variation inorientation of liquid crystal molecules such as shown in FIG. 41. Stillother arrangements are possible. Additionally, the methods can be usedto vary the orientation of LC molecules and to create a wide variety ofoptical elements comprising liquid crystal including waveplates such asswitchable waveplate (e.g., equipped with electrodes to apply electricalsignal to switch the state of the waveplate), broadband waveplates andwaveplate lenses. Additionally, although such methods can be used tovary the orientation of LC molecules in an optical element such as awaveplates, the methods can be used for other types of optical elements.Variations in the methods for fabricating the optical elements are alsopossible. For example, although imprint techniques such as nanoimprinttechniques similar to that described herein can be used, variation inthe fabrication technique as well as other approaches and fabricationtechniques may also be employed.

Additional Examples —I

1. A switchable optical assembly, comprising:

-   -   a switchable waveplate configured to be electrically activated        and deactivated to selectively alter the polarization state of        light incident thereon, said switchable waveplate comprising:        -   first and second surfaces;        -   a first liquid crystal layer disposed between said first and            second surfaces, said first liquid crystal layer comprising            a plurality of liquid crystal molecules that are rotated            about axes parallel to a central axis, said rotation varying            with an azimuthal angle about said central axis; and        -   a plurality of electrodes to apply an electrical signal            across said first liquid crystal layer.

2. The switchable optical assembly of Example 1, wherein the first andsecond surfaces comprise planar surfaces.

3. The switchable optical assembly of Examples 1 or 2, wherein the firstand second surfaces comprise planar surfaces on planar substrates.

4. The switchable optical assembly of any one of Examples 1-3, whereinthe central axis is normal to said first and second surfaces.

5. The switchable optical assembly of any one of Examples 1-4, whereineach of said liquid crystal molecules is longer than wide along alongitudinal direction and said liquid crystal molecules are rotatedabout axes parallel to said central axis such that each of the saidliquid crystal molecules has an elongated side along said longitudinaldirection that faces said central axis.

6. The switchable optical assembly of any one of Examples 1-5, whereineach of said liquid crystal molecules is longer than wide along alongitudinal direction and said liquid crystal molecules are rotatedabout axes parallel to said central axis such that said liquid crystalmolecules form concentric rings about said central axis.

7. The switchable optical assembly of any one of Examples 1-6, whereineach of said liquid crystal molecules is longer than wide along alongitudinal direction and said liquid crystal molecules are rotatedabout axes parallel to said central axis such that said longitudinaldirection is orthogonal to a radial direction from said central axis tothe said liquid crystal molecules.

8. The switchable optical assembly of any one of Examples 1-7, whereinsaid plurality of liquid crystal molecules have orientations such thatsaid plurality of liquid crystal molecules are arranged in arotationally symmetric arrangement about said central axis.

9. The switchable optical assembly of any one of Examples 1-8, whereinsaid first liquid crystal layer comprises a plurality of sublayers andsaid liquid crystal molecules are included in a first sublayer of theplurality of sublayers.

10. The switchable optical assembly of Example 9, wherein said pluralityof sublayers includes additional sublayers having liquid crystalmolecules that are positioned the same laterally or radially andoriented the same as the liquid crystal molecules included in the firstsublayer.

11. The switchable optical assembly of Example 9, wherein said pluralityof sublayers includes additional sublayers having liquid crystalmolecules positioned laterally or radially the same as the liquidcrystal molecules included in the first sublayer and progressivelytwisted about said axes parallel to the central axis, the amount oftwist increasing with increasing distance from said first sublayer.

12. The switchable optical assembly of any one of Examples 1-11, furthercomprising a second liquid crystal layer.

13. The switchable optical assembly of Example 12, wherein said secondliquid crystal layer comprises a plurality of sublayers, said pluralityof sublayers having liquid crystal molecules positioned the samelaterally or radially as the liquid crystal molecules included in thefirst sublayer of the first liquid crystal layer, said liquid crystalmolecules in said plurality of sublayers in said second liquid crystallayer progressively twisted about said axes parallel to the centralaxis, the amount of twist increasing with distance from said firstliquid crystal layer.

14. The switchable optical assembly of Examples 12 or 13, wherein saidsecond liquid crystal layer has liquid crystal molecules that aretwisted with distance from the first liquid crystal layer so as tomirror the twist of the liquid crystal molecules in the first liquidcrystal layer.

15. The switchable optical assembly of any one of Examples 12-14,wherein said first liquid crystal layer comprises a plurality ofsublayers, and wherein said second liquid crystal layer comprises aplurality of sublayers, wherein a sublayer of said second liquid crystallayer closest to the first liquid crystal layer comprises liquid crystalmolecules having substantially the same orientation as the liquidcrystal molecules in a sublayer of the first liquid crystal layer thatis closest to said second liquid crystal layer.

16. The switchable optical assembly of any one of Examples 12-15,wherein said first liquid crystal layer comprises a plurality ofsublayers, and wherein said second liquid crystal layer comprises aplurality of sublayers, wherein a sublayer of said second liquid crystallayer farthest from to the first liquid crystal layer comprises liquidcrystal molecules having substantially the same orientation as theliquid crystal molecules in a sublayer of the first liquid crystal layerthat is farthest from the second liquid crystal layer.

17. The switchable optical assembly of any one of Examples 12-16,wherein said first and second liquid crystal layers provide forincreased uniformity in altering the polarization state of lightincident thereon across multiple wavelengths in comparison to an opticalassembly having one but not the other of the first and second liquidcrystal layers.

18. The switchable optical assembly of any one of Examples 12-17,wherein said switchable waveplate is configured to diffract light at adiffraction efficiency greater than 95% within a wavelength rangeincluding at least 450 nm to 630 nm.

19. The switchable optical assembly of any one of Examples 12-18,wherein the liquid crystal molecules in said first and second liquidcrystal layers have opposite twist sense.

20. The switchable optical assembly of any one of Examples 12-19,wherein the first and second liquid crystal layers have opposite twistangles.

21. The switchable optical assembly of any one of Examples 12-20,wherein the liquid crystal molecules of the first and second liquidcrystal layers are symmetrically twisted with respect to an interfacebetween the first and second layers by a net angle between about 60degrees and 80 degrees.

22. The switchable optical assembly of any one of Examples 12-21,further comprising at least one electrode configured to apply a signalacross said second liquid crystal layer.

23. The switchable optical assembly of any one of Examples 1-22, whereinthe switchable optical assembly further comprises a first waveplate lenscomprising a liquid crystal layer, said first waveplate lens havingdifferent optical power for different polarizations of light incidentthereon, and

-   -   wherein the switchable optical assembly is configured to be        selectively switched between at least two lens states including:        -   a first lens state configured to have a first optical power,            and        -   a second lens state configured to have a second optical            power different than the first optical power.

24. The switchable optical assembly of Example 23, wherein the secondoptical power is zero optical power.

25. The switchable optical assembly of any one of Examples 1-24, whereinthe plurality of liquid crystal molecules having said rotation varyingwith the azimuthal angle about said central axis include at least 50% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid first liquid crystal layer.

26. The switchable optical assembly of any one of Examples 1-24, whereinthe plurality of liquid crystal molecules having said rotation varyingwith the azimuthal angle about said central axis include at least 50% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid first liquid crystal layer.

27. The switchable optical assembly of any one of Examples 1-24, whereinthe plurality of liquid crystal molecules having said rotation varyingwith the azimuthal angle about said central axis include at least 80% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid first liquid crystal layer.

28. The switchable optical assembly of any one of Examples 1-24, whereinthe plurality of liquid crystal molecules having said rotation varyingwith the azimuthal angle about said central axis include at least 80% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid first liquid crystal layer.

29. The switchable optical assembly of any one of Examples 1-28, whereinsaid plurality of liquid crystal molecules have orientations such thatsaid plurality of liquid crystal molecules have at least 4-foldrotational symmetry about said central axis.

30. A switchable optical assembly comprising:

-   -   a switchable waveplate configured to be electrically activated        and deactivated to selectively alter the polarization state of        light incident thereon, said switchable waveplate comprising:        -   first and second surfaces;        -   a liquid crystal layer disposed between said first and            second surfaces, said liquid crystal layer comprising a            plurality of liquid crystal molecules each longer than wide            along a longitudinal direction, said liquid crystal            molecules orientated such that said longitudinal direction            extends radially from an axis of said first and second            surfaces and said liquid crystal layer in a plurality of            radial directions from said axis; and        -   a plurality of electrodes to apply an electrical signal            across said liquid crystal layer.

31. The switchable optical assembly of Example 30, wherein the first andsecond surfaces comprise planar surfaces.

32. The switchable optical assembly of Examples 30 or 31, wherein thefirst and second surfaces comprise planar surfaces on planar substrates.

33. The switchable optical assembly of any one of Examples 30-32,wherein the axis is normal to said first and second surfaces.

34. The switchable optical assembly of any one of Examples 30-33,wherein said plurality of liquid crystal molecules are rotated aboutaxes parallel to said axis.

35. The switchable optical assembly of any one of Examples 30-34,wherein said longitudinal direction of each of said liquid crystalmolecules is parallel to said first and second surface.

36. The switchable optical assembly of any one of Examples 30-35,configured to transmit light to a viewer's eye at a distance from saidswitchable optical assembly, wherein said longitudinal directions ofeach of said liquid crystal molecules extends along respectiveprojections of the path of light from respective locations in a field ofview of the viewer's eye to the viewer's eye that are projected onto theliquid crystal layer.

37. The switchable optical assembly of any one of Examples 30-36,further comprising a waveplate lens comprising a diffractive lens.

38. The switchable optical assembly of any one of Examples 30-37,further comprising a waveplate lens comprising a liquid crystal layer,wherein the liquid crystal layer of the waveplate lens is arranged suchthat the waveplate lens has birefringence (Δn) that varies in a radiallyoutward direction from a central region of the first waveplate lens.

39. The switchable optical assembly of any one of Examples 30-38,wherein when the switchable waveplate is in a first state, theswitchable waveplate serves as a half waveplate configured to invert thehandedness of circularly polarized light passing therethrough, whilewhen the switchable waveplate is in a second state, the switchablewaveplate is configured to conserve the handedness of circularlypolarized light passing therethrough.

40. The switchable optical assembly of any one of Examples 30-39,wherein the liquid crystal layer comprises a plurality of sublayers andsaid liquid crystal molecules are included in a first sublayer of theplurality of sublayers.

41. The switchable optical assembly of Example 40, wherein saidplurality of sublayers includes additional sublayers having liquidcrystal molecules oriented and positioned the same laterally or radiallyas the liquid crystal molecules included in the first sublayer.

42. The switchable optical assembly of any one of Examples 30-41,wherein the switchable optical assembly further comprises a firstwaveplate lens comprising a liquid crystal layer, said first waveplatelens having different optical power for different polarizations of lightincident thereon, and

-   -   wherein the switchable optical assembly is configured to be        selectively switched between at least two lens states including:    -   a first lens state configured to have a first optical power; and    -   a second lens state configured to have a second optical power        different than the first optical power.

43. The switchable optical assembly of Example 42, wherein the secondoptical power is zero optical power.

44. The switchable optical assembly any one of Examples 30-43, whereinthe plurality of liquid crystal molecules orientated such thatrespective longitudinal directions extend radially from said axis in aplurality of radial directions from said axis include at least 50% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid liquid crystal layer.

45. The switchable optical assembly of any one of Examples 30-43,wherein the plurality of liquid crystal molecules orientated such thatrespective longitudinal directions extend radially from said axis in aplurality of radial directions from said axis include at least 50% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid liquid crystal layer.

46. The switchable optical assembly of any one of Examples 30-43,wherein the plurality of liquid crystal molecules orientated such thatrespective longitudinal directions extend radially from said axis in aplurality of radial directions from said axis include at least 80% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid liquid crystal layer.

47. The switchable optical assembly of any one of Examples 30-43,wherein the plurality of liquid crystal molecules orientated such thatrespective longitudinal directions extend radially from said axis in aplurality of radial directions from said axis include at least 80% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid liquid crystal layer.

48. The switchable optical assembly of any one of Examples 30-47,wherein said axis comprises a central axis of said first and secondsurfaces and said liquid crystal layer.

49. A method of fabricating an optical element, comprising:

-   -   providing a substrate extending along a horizontal direction and        having a normal thereto directed in a vertical direction;    -   providing a first vertical alignment layer;    -   providing a second horizontal alignment layer; and    -   providing a liquid crystal layer comprising liquid crystal        molecules with respect to said first vertical alignment layer        and said second horizontal alignment layer such that said liquid        crystal molecules are oriented at an oblique angle with respect        to said vertical and horizontal directions, said first vertical        alignment layer causing said liquid crystal molecules to be        oriented more vertical than without said first vertical        alignment layer and said second horizontal alignment layer        causing said liquid crystal molecules to be more horizontal than        without said second horizontal alignment layer.

50. The method of Example 49, wherein said first vertical alignmentlayer is configured to cause liquid crystal molecules proximal theretoto be oriented more along said vertical direction than said horizontaldirection.

51. The method of Examples 49 or 50, wherein said second horizontalalignment layer is configured to cause liquid crystal molecules proximalthereto to be more along said horizontal direction than said verticaldirection.

52. The method of any one of Examples 49-51, wherein said secondhorizontal alignment layer comprises a patterned layer.

53. The method of Example 52, wherein said second horizontal alignmentlayer comprises an imprint layer.

54. The method of Examples 52 or 53, wherein said second horizontalalignment layer comprises a nanoimprint layer.

55. The method of Example 54, wherein the nanoimprint layer is formedusing a nanoimprint template.

56. The method of Example 55, wherein the patterned layer is formedusing a lithography technique or an etch technique.

57. The method of any one of Examples 49-56, wherein said first verticalalignment layer and said second horizontal alignment layer are disposedover said substrate.

58. The method of any one of Examples 49-57, wherein said first verticalalignment layer is disposed between said second horizontal alignmentlayer and said substrate.

59. The method of any one of Examples 49-58, wherein said secondhorizontal alignment layer is disposed between said first verticalalignment layer and said substrate.

60. The method of any one of Examples 49-59, wherein said secondhorizontal alignment layer has first and second regions, said firstregion configured to cause said liquid crystal molecules to be morehorizontal than said second region.

61. The method of Example 60, wherein the first and second regions ofsaid second horizontal alignment layer comprise features, and whereinsaid features in said first region have a larger size than said featuresin said second region such that said liquid crystal molecules moreproximal to said first region are more horizontal than said liquidcrystal molecules more proximal to said second region.

62. The method of Examples 60 or 61, wherein the first region and secondregions of said second horizontal alignment layer comprise features, andwherein said features in said first region having a larger height thansaid features in said second region such that said liquid crystalmolecules more proximal to said first region are more horizontal thansaid liquid crystal molecules more proximal to said second region.

63. The method of any one of Examples 60-62, wherein the first andsecond regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region are wider thansaid features in said second region such that said liquid crystalmolecules more proximal to said first region are more horizontal thansaid liquid crystal molecules more proximal to said second region.

64. The method of any one of Examples 60-63, wherein the first andsecond regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have a higherpitch than said features in said second region such that said liquidcrystal molecules more proximal to said first region are more horizontalthan said liquid crystal molecules more proximal to said second region.

65. The method of any one of Examples 60-64, wherein the first andsecond regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have a higherduty cycle than said features in said second region such that saidliquid crystal molecules more proximal to said first region are morehorizontal than said liquid crystal molecules more proximal to saidsecond region.

66. The method of any one of Examples 60-65, wherein the first andsecond regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have adifferent profile than said features in said second region to cause saidliquid crystal molecules more proximal to said first region to be morehorizontal than said liquid crystal molecules more proximal to saidsecond region.

67. The method of any one of Examples 60-66, wherein the first andsecond regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have adifferent aspect ratio than said features in said second region to causesaid liquid crystal molecules more proximal to said first region to bemore horizontal than said liquid crystal molecules more proximal to saidsecond region.

68. The method of any one of Examples 49-67, wherein said secondhorizontal alignment layer comprises regions configured not to causesaid oblique angle to be more horizontal.

69. The method of any one of Examples 49-69, wherein said secondhorizontal alignment layer comprises at least one region configured notto cause said oblique angle to be more horizontal disposed between tworegions of said second horizontal alignment layer configured to causesaid oblique angle to be more horizontal.

70. The method of any of Examples 49-69, wherein said first verticalalignment layer has first and second regions, said first regionconfigured to cause said liquid crystal molecules to be more verticalthan said second region.

71. The method of Example 70, wherein the first region and secondregions of said of first horizontal alignment layer have differentthickness such that said liquid crystal molecules more proximal to saidfirst region are more vertical than liquid crystal molecules moreproximal to said second region.

72. The method of any one of Examples 49-71, wherein said first verticalalignment layer comprises regions configured not to cause said obliqueangle to be more vertical.

73. The method of any one of Examples 49-72, wherein said first verticalalignment layer comprises at least one region configured not to causesaid oblique angle to be more vertical disposed between two regions ofsaid first vertical alignment layer configured to cause said obliqueangle to be more vertical.

74. The method of any one of Examples 49-73, wherein said oblique angledepends on relative strengths of the first vertical alignment layer andthe second horizontal alignment layer.

75. The method of any of Examples 49-74, further comprising:

-   -   providing a third vertical alignment layer; and    -   providing a fourth horizontal alignment layer,    -   wherein said first vertical alignment layer causes said liquid        crystal layers to be oriented more vertical than without said        third vertical alignment layer and said fourth horizontal        alignment layer causes said liquid crystal molecules to be more        horizontal than without said fourth horizontal alignment layer.

76. The method of Example 75, wherein said liquid crystal layer isdisposed between said first and third vertical alignment layers.

77. The method of Examples 75 or 76, wherein said liquid crystal layeris disposed between said second and fourth vertical alignment layers.

78. The method of any one of Examples 49-77, wherein the oblique angleis between 0°-90° with respect to the horizontal direction.

79. The method of any one of Examples 49-77, wherein the oblique anglefor most of said liquid crystal molecules in said liquid crystal layeris between 5°-85° with respect to the horizontal direction.

80. The method of any one of Examples 49-79, wherein the oblique anglefor most of said liquid crystal molecules in said liquid crystal layeris between 5°-45° with respect to the horizontal direction.

81. The method of any one of Examples 49-80, wherein said opticalelement comprises a waveplate.

82. The method of any one of Examples 49-80, wherein said opticalelement comprises a switchable waveplate.

83. The method of any one of Examples 49-82, further comprises formingelectrodes configured to apply an electrical signal to said liquidcrystal layer.

84. The method of any one of Examples 48-83, wherein said opticalelement comprises a waveplate lens.

Additional Examples—II

1. An optical assembly, comprising:

-   -   a waveplate configured alter the polarization state of light        incident thereon, said waveplate comprising:        -   first and second surfaces;        -   a first liquid crystal layer disposed between said first and            second surfaces, said first liquid crystal layer comprising            a plurality of liquid crystal molecules that are rotated            about axes parallel to a central axis, said rotation varying            with an azimuthal angle about said central axis.

2. The optical assembly of Example 1, wherein the first and secondsurfaces comprise planar surfaces.

3. The optical assembly of Examples 1 or 2, wherein the first and secondsurfaces comprise planar surfaces on planar substrates.

4. The optical assembly of any one of Examples 1-3, wherein the centralaxis is normal to said first and second surfaces.

5. The optical assembly of any one of Examples 1-4, wherein each of saidliquid crystal molecules is longer than wide along a longitudinaldirection and said liquid crystal molecules are rotated about axesparallel to said central axis such that each of the said liquid crystalmolecules has an elongated side along said longitudinal direction thatfaces said central axis.

6. The optical assembly of any one of Examples 1-5, wherein each of saidliquid crystal molecules is longer than wide along a longitudinaldirection and said liquid crystal molecules are rotated about axesparallel to said central axis such that said liquid crystal moleculesform concentric rings about said central axis.

7. The optical assembly of any one of Examples 1-6, wherein each of saidliquid crystal molecules is longer than wide along a longitudinaldirection and said liquid crystal molecules are rotated about axesparallel to said central axis such that said longitudinal direction isorthogonal to a radial direction from said central axis to the saidliquid crystal molecules.

8. The optical assembly of any one of Examples 1-7, wherein saidplurality of liquid crystal molecules have orientations such that saidplurality of liquid crystal molecules are arranged in a rotationallysymmetric arrangement about said central axis.

9. The optical assembly of any one of Examples 1-8, wherein said firstliquid crystal layer comprises a plurality of sublayers and said liquidcrystal molecules are included in a first sublayer of the plurality ofsublayers.

10. The optical assembly of Example 9, wherein said plurality ofsublayers includes additional sublayers having liquid crystal moleculesthat are positioned the same laterally or radially and oriented the sameas the liquid crystal molecules included in the first sublayer.

11. The optical assembly of Example 9, wherein said plurality ofsublayers includes additional sublayers having liquid crystal moleculespositioned laterally or radially the same as the liquid crystalmolecules included in the first sublayer and progressively twisted aboutsaid axes parallel to the central axis, the amount of twist increasingwith increasing distance from said first sublayer.

12. The optical assembly of any one of Examples 1-11, further comprisinga second liquid crystal layer.

13. The optical assembly of Example 12, wherein said second liquidcrystal layer comprises a plurality of sublayers, said plurality ofsublayers having liquid crystal molecules positioned the same laterallyor radially as the liquid crystal molecules included in the firstsublayer of the first liquid crystal layer, said liquid crystalmolecules in said plurality of sublayers in said second liquid crystallayer progressively twisted about said axes parallel to the centralaxis, the amount of twist increasing with distance from said firstliquid crystal layer.

14. The optical assembly of Examples 12 or 13, wherein said secondliquid crystal layer has liquid crystal molecules that are twisted withdistance from the first liquid crystal layer so as to mirror the twistof the liquid crystal molecules in the first liquid crystal layer.

15. The optical assembly of any one of Examples 12-14, wherein saidfirst liquid crystal layer comprises a plurality of sublayers, andwherein said second liquid crystal layer comprises a plurality ofsublayers, wherein a sublayer of said second liquid crystal layerclosest to the first liquid crystal layer comprises liquid crystalmolecules having substantially the same orientation as the liquidcrystal molecules in a sublayer of the first liquid crystal layer thatis closest to said second liquid crystal layer.

16. The optical assembly of any one of Examples 12-15, wherein saidfirst liquid crystal layer comprises a plurality of sublayers, andwherein said second liquid crystal layer comprises a plurality ofsublayers, wherein a sublayer of said second liquid crystal layerfarthest from to the first liquid crystal layer comprises liquid crystalmolecules having substantially the same orientation as the liquidcrystal molecules in a sublayer of the first liquid crystal layer thatis farthest from the second liquid crystal layer.

17. The optical assembly of any one of Examples 12-16, wherein saidfirst and second liquid crystal layers provide for increased uniformityin altering the polarization state of light incident thereon acrossmultiple wavelengths in comparison to an optical assembly having one butnot the other of the first and second liquid crystal layers.

18. The optical assembly of any one of Examples 12-17, wherein saidwaveplate is configured to diffract light at a diffraction efficiencygreater than 95% within a wavelength range including at least 450 nm to630 nm.

19. The optical assembly of any one of Examples 12-18, wherein theliquid crystal molecules in said first and second liquid crystal layershave opposite twist sense.

20. The optical assembly of any one of Examples 12-19, wherein the firstand second liquid crystal layers have opposite twist angles.

21. The optical assembly of any one of Examples 12-20, wherein theliquid crystal molecules of the first and second liquid crystal layersare symmetrically twisted with respect to an interface between the firstand second layers by a net angle between about 60 degrees and 80degrees.

22. The optical assembly of any one of Examples 12-21, furthercomprising at least one electrode configured to apply a signal acrosssaid second liquid crystal layer.

23. The optical assembly of any one of Examples 1-22, wherein theoptical assembly further comprises a first waveplate lens comprising aliquid crystal layer, said first waveplate lens having different opticalpower for different polarizations of light incident thereon, and

-   -   wherein the optical assembly is configured to be selectively        switched between at least two lens states including:        -   a first lens state configured to have a first optical power,            and        -   a second lens state configured to have a second optical            power different than the first optical power.

24. The optical assembly of Example 23, wherein the second optical poweris zero optical power.

25. The optical assembly of any one of Examples 1-24, wherein theplurality of liquid crystal molecules having said rotation varying withthe azimuthal angle about said central axis include at least 50% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid first liquid crystal layer.

26. The optical assembly of any one of Examples 1-24, wherein theplurality of liquid crystal molecules having said rotation varying withthe azimuthal angle about said central axis include at least 50% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid first liquid crystal layer.

27. The optical assembly of any one of Examples 1-24, wherein theplurality of liquid crystal molecules having said rotation varying withthe azimuthal angle about said central axis include at least 80% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid first liquid crystal layer.

28. The optical assembly of any one of Examples 1-24, wherein theplurality of liquid crystal molecules having said rotation varying withthe azimuthal angle about said central axis include at least 80% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid first liquid crystal layer.

29. The optical assembly of any one of Examples 1-28, wherein saidplurality of liquid crystal molecules have orientations such that saidplurality of liquid crystal molecules have at least 4-fold rotationalsymmetry about said central axis.

30. An optical assembly comprising:

-   -   a waveplate configured to alter the polarization state of light        incident thereon, said waveplate comprising:        -   first and second surfaces; and        -   a liquid crystal layer disposed between said first and            second surfaces, said liquid crystal layer comprising a            plurality of liquid crystal molecules each longer than wide            along a longitudinal direction, said liquid crystal            molecules orientated such that said longitudinal direction            extends radially from an axis of said first and second            surfaces and said liquid crystal layer in a plurality of            radial directions from said axis.

31. The optical assembly of Example 30, wherein the first and secondsurfaces comprise planar surfaces.

32. The optical assembly of Examples 30 or 31, wherein the first andsecond surfaces comprise planar surfaces on planar substrates.

33. The optical assembly of any one of Examples 30-32, wherein the axisis normal to said first and second surfaces.

34. The optical assembly of any one of Examples 30-33, wherein saidplurality of liquid crystal molecules are rotated about axes parallel tosaid axis.

35. The optical assembly of any one of Examples 30-34, wherein saidlongitudinal direction of each of said liquid crystal molecules isparallel to said first and second surface.

36. The optical assembly of any one of Examples 30-35, configured totransmit light to a viewer's eye at a distance from said opticalassembly, wherein said longitudinal directions of each of said liquidcrystal molecules extends along respective projections of the path oflight from respective locations in a field of view of the viewer's eyeto the viewer's eye that are projected onto the liquid crystal layer.

37. The optical assembly of any one of Examples 30-36, furthercomprising a waveplate lens comprising a diffractive lens.

38. The optical assembly of any one of Examples 30-37, furthercomprising a waveplate lens comprising a liquid crystal layer, whereinthe liquid crystal layer of the waveplate lens is arranged such that thewaveplate lens has birefringence (Δn) that varies in a radially outwarddirection from a central region of the first waveplate lens.

39. The optical assembly of any one of Examples 30-38, wherein when thewaveplate is in a first state, the waveplate serves as a half waveplateconfigured to invert the handedness of circularly polarized lightpassing therethrough, while when the waveplate is in a second state, thewaveplate is configured to conserve the handedness of circularlypolarized light passing therethrough.

40. The optical assembly of any one of Examples 30-39, wherein theliquid crystal layer comprises a plurality of sublayers and said liquidcrystal molecules are included in a first sublayer of the plurality ofsublayers.

41. The optical assembly of Example 40, wherein said plurality ofsublayers includes additional sublayers having liquid crystal moleculesoriented and positioned the same laterally or radially as the liquidcrystal molecules included in the first sublayer.

42. The optical assembly of any one of Examples 30-41, wherein theoptical assembly further comprises a first waveplate lens comprising aliquid crystal layer, said first waveplate lens having different opticalpower for different polarizations of light incident thereon, and

-   -   wherein the optical assembly is configured to be selectively        switched between at least two lens states including:    -   a first lens state configured to have a first optical power; and    -   a second lens state configured to have a second optical power        different than the first optical power.

43. The optical assembly of Example 42, wherein the second optical poweris zero optical power.

44. The optical assembly any one of Examples 30-43, wherein theplurality of liquid crystal molecules orientated such that respectivelongitudinal directions extend radially from said axis in a plurality ofradial directions from said axis include at least 50% of liquid crystalmolecules extending over a range of at least 1 cm² across said liquidcrystal layer.

45. The optical assembly of any one of Examples 30-43, wherein theplurality of liquid crystal molecules orientated such that respectivelongitudinal directions extend radially from said axis in a plurality ofradial directions from said axis include at least 50% of liquid crystalmolecules extending over a range of at least 2 cm² across said liquidcrystal layer.

46. The optical assembly of any one of Examples 30-43, wherein theplurality of liquid crystal molecules orientated such that respectivelongitudinal directions extend radially from said axis in a plurality ofradial directions from said axis include at least 80% of liquid crystalmolecules extending over a range of at least 1 cm² across said liquidcrystal layer.

47. The optical assembly of any one of Examples 30-43, wherein theplurality of liquid crystal molecules orientated such that respectivelongitudinal directions extend radially from said axis in a plurality ofradial directions from said axis include at least 80% of liquid crystalmolecules extending over a range of at least 2 cm² across said liquidcrystal layer.

48. The optical assembly of any one of Examples 30-47, wherein said axiscomprises a central axis of said first and second surfaces and saidliquid crystal layer.

49. An optical element, comprising:

-   -   a substrate extending along a horizontal direction and having a        normal thereto directed in a vertical direction;    -   a first vertical alignment layer;    -   a second horizontal alignment layer; and    -   a liquid crystal layer comprising liquid crystal molecules with        respect to said first vertical alignment layer and said second        horizontal alignment layer such that said liquid crystal        molecules are oriented at an oblique angle with respect to said        vertical and horizontal directions, said first vertical        alignment layer causing said liquid crystal molecules to be        oriented more vertical than without said first vertical        alignment layer and said second horizontal alignment layer        causing said liquid crystal molecules to be more horizontal than        without said second horizontal alignment layer.

50. The optical element of Example 49, wherein said first verticalalignment layer is configured to cause liquid crystal molecules proximalthereto to be oriented more along said vertical direction than saidhorizontal direction.

51. The optical element of Examples 49 or 50, wherein said secondhorizontal alignment layer is configured to cause liquid crystalmolecules proximal thereto to be more along said horizontal directionthan said vertical direction.

52. The optical element of any one of Examples 49-51, wherein saidsecond horizontal alignment layer comprises a patterned layer.

53. The optical element of Example 52, wherein said second horizontalalignment layer comprises an imprint layer.

54. The optical element of Examples 52 or 53, wherein said secondhorizontal alignment layer comprises a nanoimprint layer.

55. The optical element of Example 54, wherein the nanoimprint layer isformed using a nanoimprint template.

56. The optical element of Example 55, wherein the patterned layer isformed using a lithography technique or an etch technique.

57. The optical element of any one of Examples 49-56, wherein said firstvertical alignment layer and said second horizontal alignment layer aredisposed over said substrate.

58. The optical element of any one of Examples 49-57, wherein said firstvertical alignment layer is disposed between said second horizontalalignment layer and said substrate.

59. The optical element of any one of Examples 49-58, wherein saidsecond horizontal alignment layer is disposed between said firstvertical alignment layer and said substrate.

60. The optical element of any one of Examples 49-59, wherein saidsecond horizontal alignment layer has first and second regions, saidfirst region configured to cause said liquid crystal molecules to bemore horizontal than said second region.

61. The optical element of Example 60, wherein the first and secondregions of said second horizontal alignment layer comprise features, andwherein said features in said first region have a larger size than saidfeatures in said second region such that said liquid crystal moleculesmore proximal to said first region are more horizontal than said liquidcrystal molecules more proximal to said second region.

62. The optical element of Examples 60 or 61, wherein the first regionand second regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region having a largerheight than said features in said second region such that said liquidcrystal molecules more proximal to said first region are more horizontalthan said liquid crystal molecules more proximal to said second region.

63. The optical element of any one of Examples 60-62, wherein the firstand second regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region are wider thansaid features in said second region such that said liquid crystalmolecules more proximal to said first region are more horizontal thansaid liquid crystal molecules more proximal to said second region.

64. The optical element of any one of Examples 60-63, wherein the firstand second regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have a higherpitch than said features in said second region such that said liquidcrystal molecules more proximal to said first region are more horizontalthan said liquid crystal molecules more proximal to said second region.

65. The optical element of any one of Examples 60-64, wherein the firstand second regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have a higherduty cycle than said features in said second region such that saidliquid crystal molecules more proximal to said first region are morehorizontal than said liquid crystal molecules more proximal to saidsecond region.

66. The optical element of any one of Examples 60-65, wherein the firstand second regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have adifferent profile than said features in said second region to cause saidliquid crystal molecules more proximal to said first region to be morehorizontal than said liquid crystal molecules more proximal to saidsecond region.

67. The optical element of any one of Examples 60-66, wherein the firstand second regions of said second horizontal alignment layer comprisefeatures, and wherein said features in said first region have adifferent aspect ratio than said features in said second region to causesaid liquid crystal molecules more proximal to said first region to bemore horizontal than said liquid crystal molecules more proximal to saidsecond region.

68. The optical element of any one of Examples 49-67, wherein saidsecond horizontal alignment layer comprises regions configured not tocause said oblique angle to be more horizontal.

69. The optical element of any one of Examples 49-69, wherein saidsecond horizontal alignment layer comprises at least one regionconfigured not to cause said oblique angle to be more horizontaldisposed between two regions of said second horizontal alignment layerconfigured to cause said oblique angle to be more horizontal.

70. The optical element of any of Examples 49-69, wherein said firstvertical alignment layer has first and second regions, said first regionconfigured to cause said liquid crystal molecules to be more verticalthan said second region.

71. The optical element of Example 70, wherein the first region andsecond regions of said of first horizontal alignment layer havedifferent thickness such that said liquid crystal molecules moreproximal to said first region are more vertical than liquid crystalmolecules more proximal to said second region.

72. The optical element of any one of Examples 49-71, wherein said firstvertical alignment layer comprises regions configured not to cause saidoblique angle to be more vertical.

73. The optical element of any one of Examples 49-72, wherein said firstvertical alignment layer comprises at least one region configured not tocause said oblique angle to be more vertical disposed between tworegions of said first vertical alignment layer configured to cause saidoblique angle to be more vertical.

74. The optical element of any one of Examples 49-73, wherein saidoblique angle depends on relative strengths of the first verticalalignment layer and the second horizontal alignment layer.

75. The optical element of any of Examples 49-74, further comprising:

-   -   a third vertical alignment layer; and    -   a fourth horizontal alignment layer,    -   wherein said first vertical alignment layer causes said liquid        crystal layers to be oriented more vertical than without said        third vertical alignment layer and said fourth horizontal        alignment layer causes said liquid crystal molecules to be more        horizontal than without said fourth horizontal alignment layer.

76. The optical element of Example 75, wherein said liquid crystal layeris disposed between said first and third vertical alignment layers.

77. The optical element of Examples 75 or 76, wherein said liquidcrystal layer is disposed between said second and fourth verticalalignment layers.

78. The optical element of any one of Examples 49-77, wherein theoblique angle is between 0°-90° with respect to the horizontaldirection.

79. The optical element of any one of Examples 49-77, wherein theoblique angle for most of said liquid crystal molecules in said liquidcrystal layer is between 5°-85° with respect to the horizontaldirection.

80. The optical element of any one of Examples 49-79, wherein theoblique angle for most of said liquid crystal molecules in said liquidcrystal layer is between 5°-45° with respect to the horizontaldirection.

81. The optical element of any one of Examples 49-80, wherein saidoptical element comprises a waveplate.

82. The optical element of any one of Examples 49-80, wherein saidoptical element comprises a switchable waveplate.

83. The optical element of any one of Examples 49-82, further comprisesforming electrodes configured to apply an electrical signal to saidliquid crystal layer.

84. The optical element of any one of Examples 48-83, wherein saidoptical element comprises a waveplate lens.

85. The optical assembly of any one of Examples 1-29, wherein thewaveplate is a switchable waveplate comprising a plurality of electrodesconfigured to apply an electrical signal across said first liquidcrystal layer such that the switchable waveplate is configured to beelectrically activated and deactivated to selectively alter thepolarization state of light incident thereon.

86. The optical assembly of any one of Examples 30-48, wherein thewaveplate is a switchable waveplate comprising a plurality of electrodesconfigured to apply an electrical signal across said first liquidcrystal layer such that the switchable waveplate is configured to beelectrically activated and deactivated to selectively alter thepolarization state of light incident thereon.

ADDITIONAL CONSIDERATIONS

In the foregoing specification, the invention has been described withreference to specific embodiments thereof. It will, however, be evidentthat various modifications and changes may be made thereto withoutdeparting from the broader spirit and scope of the invention. Thespecification and drawings are, accordingly, to be regarded in anillustrative rather than restrictive sense.

Indeed, it will be appreciated that the systems and methods of thedisclosure each have several innovative aspects, no single one of whichis solely responsible or required for the desirable attributes disclosedherein. The various features and processes described above may be usedindependently of one another, or may be combined in various ways. Allpossible combinations and subcombinations are intended to fall withinthe scope of this disclosure. For example, referring to FIG. 15, it willbe appreciated that one or more adaptive lens assemblies 1504-1 to1504-3 may be disposed between individual ones of the waveguides 1012 a,1012 b, and/or 1012 c.

Certain features that are described in this specification in the contextof separate embodiments also may be implemented in combination in asingle embodiment. Conversely, various features that are described inthe context of a single embodiment also may be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination may in some cases be excised from thecombination, and the claimed combination may be directed to asubcombination or variation of a subcombination. No single feature orgroup of features is necessary or indispensable to each and everyembodiment.

It will be appreciated that conditional language used herein, such as,among others, “can,” “could,” “might,” “may,” “e.g.,” and the like,unless specifically stated otherwise, or otherwise understood within thecontext as used, is generally intended to convey that certainembodiments include, while other embodiments do not include, certainfeatures, elements and/or steps. Thus, such conditional language is notgenerally intended to imply that features, elements and/or steps are inany way required for one or more embodiments or that one or moreembodiments necessarily include logic for deciding, with or withoutauthor input or prompting, whether these features, elements and/or stepsare included or are to be performed in any particular embodiment. Theterms “comprising,” “including,” “having,” and the like are synonymousand are used inclusively, in an open-ended fashion, and do not excludeadditional elements, features, acts, operations, and so forth. Also, theterm “or” is used in its inclusive sense (and not in its exclusivesense) so that when used, for example, to connect a list of elements,the term “or” means one, some, or all of the elements in the list. Inaddition, the articles “a,” “an,” and “the” as used in this applicationand the appended claims are to be construed to mean “one or more” or “atleast one” unless specified otherwise. Similarly, while operations maybe depicted in the drawings in a particular order, it is to berecognized that such operations need not be performed in the particularorder shown or in sequential order, or that all illustrated operationsbe performed, to achieve desirable results. Further, the drawings mayschematically depict one more example processes in the form of aflowchart. However, other operations that are not depicted may beincorporated in the example methods and processes that are schematicallyillustrated. For example, one or more additional operations may beperformed before, after, simultaneously, or between any of theillustrated operations. Additionally, the operations may be rearrangedor reordered in other embodiments. In certain circumstances,multitasking and parallel processing may be advantageous. Moreover, theseparation of various system components in the embodiments describedabove should not be understood as requiring such separation in allembodiments, and it should be understood that the described programcomponents and systems may generally be integrated together in a singlesoftware product or packaged into multiple software products.Additionally, other embodiments are within the scope of the followingclaims. In some cases, the actions recited in the claims may beperformed in a different order and still achieve desirable results.

Accordingly, the claims are not intended to be limited to theembodiments shown herein, but are to be accorded the widest scopeconsistent with this disclosure, the principles and the novel featuresdisclosed herein.

1. A switchable optical assembly, comprising: a switchable waveplateconfigured to be electrically activated and deactivated to selectivelyalter the polarization state of light incident thereon, said switchablewaveplate comprising: first and second surfaces; a first liquid crystallayer disposed between said first and second surfaces, said first liquidcrystal layer comprising a plurality of liquid crystal molecules thatare rotated about respective axes parallel to a central axis, saidrotation varying with an azimuthal angle about said central axis; and aplurality of electrodes to apply an electrical signal across said firstliquid crystal layer.
 2. The switchable optical assembly of claim 1,wherein the first and second surfaces comprise planar surfaces.
 3. Theswitchable optical assembly of claim 1, wherein the first and secondsurfaces comprise planar surfaces on planar substrates.
 4. Theswitchable optical assembly of claim 1, wherein the central axis isnormal to said first and second surfaces.
 5. The switchable opticalassembly of claim 1, wherein said liquid crystal molecules are longerthan wide along respective longitudinal directions and said liquidcrystal molecules are rotated about respective axes parallel to saidcentral axis such that said liquid crystal molecules have respectiveelongated sides along said respective longitudinal directions that facesaid central axis.
 6. The switchable optical assembly of claim 1,wherein said liquid crystal molecules are longer than wide along arespective longitudinal directions and said liquid crystal molecules arerotated about respective axes parallel to said central axis such thatsaid liquid crystal molecules form one or more concentric rings aboutsaid central axis.
 7. The switchable optical assembly of claim 1,wherein said liquid crystal molecules are longer than wide alongrespective longitudinal directions and said liquid crystal molecules arerotated about respective axes parallel to said central axis such thatsaid respective longitudinal direction are orthogonal to a radialdirection from said central axis to the said liquid crystal molecules.8. The switchable optical assembly of claim 1, wherein said plurality ofliquid crystal molecules have orientations such that said plurality ofliquid crystal molecules are arranged in a rotationally symmetricarrangement about said central axis.
 9. The switchable optical assemblyof claim 1, wherein said first liquid crystal layer comprises aplurality of sublayers and said liquid crystal molecules are included ina first sublayer of the plurality of sublayers.
 10. The switchableoptical assembly of claim 9, wherein said plurality of sublayersincludes additional sublayers having liquid crystal molecules that arepositioned the same laterally or radially and oriented the same as theliquid crystal molecules included in the first sublayer.
 11. Theswitchable optical assembly of claim 9, wherein said plurality ofsublayers includes additional sublayers having liquid crystal moleculespositioned laterally or radially the same as the liquid crystalmolecules included in the first sublayer and progressively twisted aboutsaid axes parallel to the central axis, the amount of twist increasingwith increasing distance from said first sublayer.
 12. The switchableoptical assembly of claim 1, further comprising a second liquid crystallayer.
 13. The switchable optical assembly of claim 12, wherein saidsecond liquid crystal layer comprises a plurality of sublayers, saidplurality of sublayers having liquid crystal molecules positioned thesame laterally or radially as the liquid crystal molecules included inthe first sublayer of the first liquid crystal layer, said liquidcrystal molecules in said plurality of sublayers in said second liquidcrystal layer progressively twisted about said axes parallel to thecentral axis, the amount of twist increasing with distance from saidfirst liquid crystal layer.
 14. The switchable optical assembly of claim12, wherein said second liquid crystal layer has liquid crystalmolecules that are twisted with distance from the first liquid crystallayer so as to mirror the twist of the liquid crystal molecules in thefirst liquid crystal layer.
 15. The switchable optical assembly of claim12, wherein said first liquid crystal layer comprises a plurality ofsublayers, and wherein said second liquid crystal layer comprises aplurality of sublayers, wherein a sublayer of said second liquid crystallayer closest to the first liquid crystal layer comprises liquid crystalmolecules having substantially the same orientation as the liquidcrystal molecules in a sublayer of the first liquid crystal layer thatis closest to said second liquid crystal layer.
 16. The switchableoptical assembly of claim 12, wherein said first liquid crystal layercomprises a plurality of sublayers, and wherein said second liquidcrystal layer comprises a plurality of sublayers, wherein a sublayer ofsaid second liquid crystal layer farthest from to the first liquidcrystal layer comprises liquid crystal molecules having substantiallythe same orientation as the liquid crystal molecules in a sublayer ofthe first liquid crystal layer that is farthest from the second liquidcrystal layer.
 17. The switchable optical assembly of claim 12, whereinsaid first and second liquid crystal layers provide for increaseduniformity in altering the polarization state of light incident thereonacross multiple wavelengths in comparison to an optical assembly havingone but not the other of the first and second liquid crystal layers. 18.The switchable optical assembly of claim 12, wherein said switchablewaveplate is configured to diffract light at a diffraction efficiencygreater than 95% within a wavelength range including at least 450 nm to630 nm.
 19. The switchable optical assembly of claim 12, wherein theliquid crystal molecules in said first and second liquid crystal layershave opposite twist sense.
 20. The switchable optical assembly of claim12, wherein the first and second liquid crystal layers have oppositetwist angles.
 21. The switchable optical assembly of claim 12, whereinthe liquid crystal molecules of the first and second liquid crystallayers are symmetrically twisted with respect to an interface betweenthe first and second layers by a net angle between about 60 degrees and80 degrees.
 22. The switchable optical assembly of claim 12, furthercomprising at least one electrode configured to apply a signal acrosssaid second liquid crystal layer.
 23. The switchable optical assembly ofclaim 1, wherein the switchable optical assembly further comprises afirst waveplate lens comprising a liquid crystal layer, said firstwaveplate lens having different optical power for differentpolarizations of light incident thereon, and wherein the switchableoptical assembly is configured to be selectively switched between atleast two lens states including: a first lens state configured to have afirst optical power, and a second lens state configured to have a secondoptical power different than the first optical power.
 24. The switchableoptical assembly of claim 23, wherein the second optical power is zerooptical power.
 25. The switchable optical assembly of claim 1, whereinthe plurality of liquid crystal molecules having said rotation varyingwith the azimuthal angle about said central axis include at least 50% ofliquid crystal molecules extending over a range of at least 1 cm² acrosssaid first liquid crystal layer.
 26. The switchable optical assembly ofclaim 1, wherein the plurality of liquid crystal molecules having saidrotation varying with the azimuthal angle about said central axisinclude at least 50% of liquid crystal molecules extending over a rangeof at least 2 cm² across said first liquid crystal layer.
 27. Theswitchable optical assembly of claim 1, wherein the plurality of liquidcrystal molecules having said rotation varying with the azimuthal angleabout said central axis include at least 80% of liquid crystal moleculesextending over a range of at least 1 cm² across said first liquidcrystal layer.
 28. The switchable optical assembly of claim 1, whereinthe plurality of liquid crystal molecules having said rotation varyingwith the azimuthal angle about said central axis include at least 80% ofliquid crystal molecules extending over a range of at least 2 cm² acrosssaid first liquid crystal layer.
 29. The switchable optical assembly ofclaim 1, wherein said plurality of liquid crystal molecules haveorientations such that said plurality of liquid crystal molecules haveat least 4-fold rotational symmetry about said central axis. 30-84.(canceled)